Bare Demo of IEEEtran.cls for Computer Society Conferences
Suhas Sreehari$^{1
*
Michael~Shell
~\IEEEmembership{Member
~IEEE
....lastname \thanks{...
\IEEEauthorblockN{Michael Shell
\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1
The abstract goes here.
CVPR_2017_arXiv.tex
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%%%%%%%%% TITLE
\title{Multi-Resolution Data Fusion for Super-Resolution Electron Microscopy}

\author{Suhas Sreehari$^{1,*}$, S. V. Venkatakrishnan$^2$, Katherine L. Bouman$^3$, Jeffrey P. Simmons$^4$,\\ Lawrence F. Drummy$^4$, and Charles A. Bouman$^1$\\
{\small $^1$School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN}\\
{\small $^2$ISML, Oak Ridge National Laboratory, Oak Ridge, TN}\\
{\small $^3$CSAIL, Massachusetts Institute of Technology, Cambridge, MA}\\
{\small $^4$Air Force Research Laboratory, Dayton, OH}\\
{\tt\small $^*$ ssreehar@purdue.edu}
}

\date{}

%\thispagestyle{empty}

\twocolumn[{%
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\maketitle
\begin{center}
    \centering
    \includegraphics[width=1\textwidth]{figs/teaser_figure}
    \captionof{figure}{
An illustration of the proposed multi-resolution data fusion (MDF) system
in which a transmission electron microscope is specially configured to collect both low resolution data over a large field-of-view (FoV)
together with a small set of high resolution patches from the same sample.
The MDF algorithm uses the high-resolution patches as an image model within the ``plug-and-play'' framework
to synthesize the 8x interpolated super-resolution output image over the full FoV.
We demonstrate the MDF system using an aberration-corrected FEI Titan transmission electron microscope
and show that it can dramatically speed up image acquisition and reduce dosage as compared to conventional homogeneous raster-scanning microscopy.
}
\end{center}%
}]
\nopagebreak

%%%%%%%%% ABSTRACT
\begin{abstract}
\vspace{-3mm}
{\small \textit{Perhaps surprisingly, the total electron microscopy (EM) data collected to date is less than a cubic millimeter.
Consequently, there is an enormous demand in the materials and biological sciences 
to image at greater speed and lower dosage, while maintaining resolution.
Traditional EM imaging based on homogeneous raster-order scanning severely limits the volume 
of high-resolution data that can be collected, 
and presents a fundamental limitation to understanding physical processes such as material deformation, crack propagation, and pyrolysis.}}

{\small \textit{We introduce a novel multi-resolution data fusion (MDF) method for super-resolution computational EM.
Our method combines innovative data acquisition with novel algorithmic techniques 
to dramatically improve the resolution/volume/speed trade-off. 
The key to our approach is to collect the entire sample at low resolution,
while simultaneously collecting a small fraction of data at high resolution.
The high-resolution measurements are then used to create a material-specific patch-library that is used 
within the ``plug-and-play'' framework to dramatically improve super-resolution of the low-resolution data.
We present results using FEI electron microscope data that demonstrate 
super-resolution factors of 4x, 8x, and 16x, 
while substantially maintaining high image quality and reducing dosage.}}
\end{abstract}


%%%%%%%%% BODY TEXT
\section{Introduction}

Scanning transmission electron microscopes are widely used for characterization of samples at the nano-meter scale. 
However, raster scanning an electron beam across a large field of view is time consuming and can often damage the sample. 
In fact, the sum total of all electron microscopy (EM) data collected to date, represents less than a cubic millimeter of material \cite{williams1996transmission}. 
This fact encapsulates a central challenge of materials and biological sciences to image larger volumes at higher resolution, greater speed, and lower dosage. 

Traditional microscopy based on homogeneous raster-order single-resolution scanning severely limits the volume of high resolution data that can be collected, and represents a fundamental limitation in understanding physical processes such as material deformation, crack propagation, and pyrolysis. 
For these reasons, there is growing interest in reconstructing full-resolution images 
from sparsely-sampled \cite{inpaintReviewSPM14, hyrumEI13, carinSparseInterp14} and low-resolution images \cite{farsiu2004fast, park2003super, glasner2009super, shechtman2005space}.

In many cases, EM samples contain repeating structures that are similar or identical to each other.
This presents enormous redundancy in conventional data acquisition methods, 
and consequently an opportunity to design imaging systems with sparse/low-resolution samples.

In this paper, we introduce a novel computational EM imaging method based on multi-resolution data fusion (MDF) that combines innovative data acquisition with novel algorithmic techniques to dramatically improve the resolution/volume/speed trade-off as compared to traditional EM imaging methods. 
Measuring fewer samples also leads to lower dosage and less sample damage, which is crucial for imaging modalities like cryo-EM.
The key to our approach is the acquisition of sparse measurements at both low and high resolutions from which a full high-resolution image is formed.
The speedup in data acquisition results from the fact that we sparsely sample the bulk of the material while densely sampling only a small-but-representative fraction of the material -- instead of making dense high-resolution measurements across the whole material.
The high-resolution measurements are then used to create a material-specific probabilistic model in the form of a patch-library that is used to dramatically increase resolution. 

Our method depends on a Bayesian framework for the fusion of low- and high-resolution data without the need for training.
The key step in our solution is to use our library-based non-local means (LB-NLM) denoising filter as a prior model within the P\&P framework 
\cite{venkatakrishnan2013school, sreehari2016TCI} -- to produce visually true textures and edge features in image interpolations, while significantly reducing mean squared error and artifacts such as ``jaggies''. 

The P\&P framework is based on the alternating direction method of multipliers 
(ADMM) \cite{gabay1976dual, eckstein1992douglas, boyd2011distributed} and decouples the forward model  
and the prior terms in the maximum \textit{a} posteriori cost function. 
This results in an algorithm that involves repeated application of two steps: 
an inversion step only dependent on the forward model, and a denoising step only dependent on the image prior model.
The P\&P takes ADMM one step further by replacing the prior model optimization by a denoising operator of choice.

We present super-resolution and sparse interpolation results on real microscope images demonstrating data acquisition speedups of 15x to 228x on various datasets, while substantially maintaining image quality. 
The speedup factors are calculated as the ratio of the number of reconstructed pixels to the number of measured pixels.
We compare our results them with cubic interpolation and Technion's single-image super-resolution (SISR) algorithm \cite{zeyde2010single}.

\section{Related Work}
\label{section:related_work}

Image interpolation and super-resolution have been widely studied to enable high-quality imaging with fewer measurements, leading to faster and cheaper data acquisition.
Spurred by the success of denoising filters like non-local means (NLM) \cite{buades2005review, chan2014monte} in exploiting non-local redundancies, 
there have been several efforts to solve the sparse image interpolation problem using patch-based models \cite{eladHarAna05, dong2013sparse, carinSparseInterp14, sapiroGMMTIP15}.
Dictionary learning \cite{zeyde2010single, yang2010image, yang2008image} and example-based methods \cite{freeman2002example} have also been proposed for achieving super-resolution from low-resolution measurements. 
Zhang et al. \cite{zhang2012single} proposed a steering kernel regression framework \cite{takeda2007kernel} to use non-local means to achieve super-resolution.
Atkins et al. \cite{atkins1999tree} proposed tree-based resolution synthesis using a regression tree as a piece-wise linear approximation to the conditional mean of the high-resolution image given the low-resolution image.
More recently, Timofte et al. \cite{timofte2015seven} discussed the use of libraries of structures and image self-similarity to improve super-resolution, but these methods involved extensive training.
Another training-based approach to super-resolution was proposed by Perez-Pellitero et al. \cite{perez2016psyco} where they derive a regression-based manifold mapping between low- and high-resolution images.

Apart from these specific solutions for image interpolation and super-resolution, Sreehari et al. \cite{sreehari2016TCI} proposed a generic Bayesian framework called ``plug-and-play'' priors (P\&P) for incorporating modern denoising algorithms as prior models in a variety of inverse problems such as sparse image interpolation.
In this spirit, Brifman et al. \cite{brifman2016turning} have adopted the P\&P framework to use sparse-coding and dictionary-learning-based denoisers for achieving super-resolution.
In any case, no method that we know of currently exists to fuse sparse/low-resolution data with dense/high-resolution measurements to form full high-resolution images without training.

\vspace{-3mm}

\section{Method}
\label{section:method}

We present a new computational imaging method for fast acquisition of high-resolution EM images. 
Our proposed acquisition method scans the image at low resolution while simultaneously collecting a small-but-representative portion of the sample at a higher resolution. This is central to achieving the data acquisition speed-up. 
Then, we fuse the low- and high-resolution images to synthesize high resolution over the full field-of-view (FoV). In this section we describe the algorithm used to fuse the low- and high-resolution images. 
We construct a high-quality patch library containing typical textures and edge features from the high-resolution portion. 
In order to use such a library as an image model, in Sec.~\ref{section:LBNLM} we construct a version of the non-local means denoiser that uses patches from the high-resolution library.
We then use our library-based non-local means (LB-NLM) denoiser as an image/prior model within the P\&P framework (see Sec.~\ref{section:PNP}).
Using the P\&P framework, we super-resolve the low-resolution image acquired over large areas of the sample through Bayesian inversion, creating a high-resolution image over the full FoV.

\subsection{The Plug-and-Play (P\&P) Framework}
\label{section:PNP}

Let $x \in \mathbb{R}^N$ be an unknown image with a prior distribution $p(x)$,
and let $y \in \mathbb{R}^M$ be the sparsely subsampled image
with conditional distribution $p(y|x)$, which is often referred to as the forward model for the sampling system.
Then the MAP estimate of the image $x$ conditioned on the sparse/low-resolution image $y$ is given by
\begin{eqnarray}
\label{eq:MAPEst}
\hat{x}_{MAP} = \argmin_{x \in \mathbb{R}^N} \{ l(x) + \beta s(x)\},
\end{eqnarray}
where $l( x) = -\log p(y|x)$, $\beta s(x) = -\log p(x)$,
and $\beta > 0$ is a parameter used to control the regularization in the MAP reconstruction.
In order to use flexible prior models to solve ill-posed inverse problems, it is helpful to separate the forward model inversion from the prior model.
This can be effectively achieved through the application of ADMM.
The first step in applying ADMM for solving equation~\eqref{eq:MAPEst} is to split the variable $x$, resulting in an equivalent expression for the MAP estimate given by
\begin{eqnarray}
\label{eq:MAPEst_reformed}
(\hat{x}, \hat{v}) = \arg \mathop{\min_{x, v \in \mathbb{R}^N }}_{ x=v } \{l(x) + \beta s(v)\} \ .
\end{eqnarray}
This constrained optimization problem has an associated scaled-form augmented Lagrangian \cite[Section 3.1.1]{boyd2011distributed},  
\begin{eqnarray}
\label{eq:Lagrangian}
L_{\lambda}(x, v; u) = l(x) + \beta s(v) + \frac{1}{2\sigma_{\lambda}^2}\|x - v + u\|_2^2 - \frac{\|u\|^2_2}{2 \sigma_\lambda^2},
\end{eqnarray}
where $\sigma_\lambda$ is the augmented Lagrangian parameter.

The ADMM algorithm consists of iteratively minimizing the augmented Lagrangian with respect to the split variables, $x$ and $v$, followed by updating the dual variable, $u$, that drives the solution toward the constraint, $x=v$.
\begin{eqnarray}
\hat{x} &\leftarrow& \arg \min_{x\in \mathbb{R}^N } L_{\lambda}(x, \hat{v}; u) \\
\hat{v} &\leftarrow& \arg \min_{v\in \mathbb{R}^N } L_{\lambda}(\hat{x}, v ; u) \\
u &\leftarrow& u + (\hat{x} - \hat{v}) \ ,
\end{eqnarray}
where $\hat{v}$ can be initialized to a baseline reconstruction and $u$ is initialized to zero. 
By letting $\tilde{x} = v - u$, and $\tilde{v} = x + u$, 
we can define two operators that help solve  Eqs.~(4) and (5).
The first is an inversion operator $F$ defined by
\begin{eqnarray}
\label{eq:F}
F(\tilde x; \sigma_{\lambda}) = \argmin_{x \in \mathbb{R}^N } \left\{ l(x) + \frac{\|x - \tilde x\|_2^2}{2\sigma_{\lambda}^2} \right\} \ ;
\end{eqnarray}
and the second is a denoising operator $H$ given by
\begin{eqnarray}
\label{eq:H}
H(\tilde{v}; \sigma_n) = \argmin_{v \in \mathbb{R}^N} \left\{ \displaystyle\frac{\|\tilde{v}-v\|_2^2}{2\sigma_n^2} + s(v) \right\} \ ;
\end{eqnarray}
where $\sigma_n = \sqrt{\beta} \sigma_{\lambda}$ has the interpretation of being
the assumed noise standard deviation in the denoising operator.
Moreover, $H$ is the proximal mapping for the proper, closed, and convex function $s:\mathbb{R}^N \rightarrow \mathbb{R}\cup \{ +\infty \}$.

Using these two operators, we can easily derive the plug-and-play algorithm
shown in Fig.~\ref{fig:PlugAndPlayAlgorithm}.

\begin{figure}[h!]
\centerline{\fbox{\parbox{5 cm}{
\begin{itemize}
\setlength\itemsep{0.5mm}
\item[] initialize $\hat{v}$ 
\item[] $u \leftarrow 0$ 
\item[] Repeat $\{$
\vspace{-2mm}
\begin{eqnarray*}
\tilde x &\leftarrow& \hat v - u \\
\hat{x} &\leftarrow& F(\tilde{x}; \sigma_{\lambda}) \\
\tilde{v} &\leftarrow& \hat{x} + u \\
\hat{v} &\leftarrow& H(\tilde{v}; \sigma_n) \\
u &\leftarrow& u + (\hat{x} - \hat{v}) \\
\end{eqnarray*}
\vspace{-14mm}
\item[] $\}$
\end{itemize}
}}}
\caption{Plug-and-play algorithm for implementation of a general forward model $F( \tilde{x} ; \sigma_\lambda )$,
and a prior model specified by the denoising operator in $H( \tilde{v} ; \sigma_n )$.} 
\label{fig:PlugAndPlayAlgorithm}
\end{figure}

In theory, the value of $\sigma_{\lambda}$ does not affect the solution computed by the P\&P algorithm;
however, in practice a poor choice may slow convergence.
Sreehari et al. \cite{sreehari2016TCI} suggest setting the value of $\sigma_{\lambda}$ based on the amount of variation in a baseline reconstruction\footnote{In our experiments, the baseline reconstructions are Shepard or cubic interpolations.}, 
\vspace{-3mm}
\begin{equation}
\label{eq:sigma_lambda}
\sigma_\lambda^2 \approx \frac{1}{N} \sum_{i=0}^{N-1} \mathrm{var} [ x_i | y ] \ .
\end{equation}

\vspace{-5mm}

\subsection{Library-Based Non-Local Means}
\label{section:LBNLM}

Access to high-quality patches can increase the effectiveness of non-local means (NLM) as a prior model.
However, in conventional implementations of NLM, we are limited by the degraded patches present in the image. 
To remove this limitation, in this section, we outline a library-based non-local means (LB-NLM) algorithm.

Our solution is to use an external library of densely-sampled/high-resolution patches that contain typical textures and edge features.
We then compute the weighted mean of the center pixels of these patches.
Computation of the weighted mean is identical to standard non-local means, only the patches do not come from the image we are denoising. The weight normalization is also identical to standard NLM weight normalization, and is therefore simpler than the symmetric normalization (see \cite{sreehari2016TCI}).

If we denote the $N_p\times N_p$ patch centered at position $s$ by $P_s$, and the $r$-th patch of the library by $L_r$, we can compute the LB-NLM weights as
\begin{eqnarray}
w_{s,r} &\gets& \exp{\left\{ \displaystyle \frac{-\|P_s - L_r\|_2^2}{2 N_p^2 \sigma_n^2}\right\}} \\[10pt]
w_{s, r} &\gets& \frac{ w_{s, r} }{ \displaystyle \sum_{r=1}^{N_l} w_{s, r} },
\end{eqnarray}
where $N_l$ is the number of patches in the library.

\noindent Further, the LB-NLM filtering is given by,
\vspace{-1mm}
\begin{equation}
\hat{v}_s = \displaystyle \sum_{r=1}^{N_l} w_{s, r} z_r,
\end{equation}
where $\hat{v}_s$ is the denoised pixel at position $s$, and $z_r$ is the center pixel of library patch $L_r$.

We use the LB-NLM denoiser as an implicit prior model within the P\&P algorithm.
When the patch library contains high-resolution, typical textures and edge features, 
using LB-NLM as a prior model enables reproduction of visually-accurate textures and edges in the reconstructed image. 

Denoising sparse/low-resolution images with the aid of dense/high-resolution patches is, in fact, how we implement the multi-resolution data fusion in every step of the P\&P algorithm.


\subsection{Super-Resolution Forward Model}
\label{section:SR}

In this section, we formulate the explicit form of the inversion operator, $F( x, \sigma_\lambda )$,
for the application of super-resolution.
Our objective will be to interpolate an image $y\in \mathbb{R}^M$ to its higher resolution version, $x\in \mathbb{R}^N$, where $M \ll N$.
The forward model for this problem is given by
\vspace{-2mm}
\begin{equation}
\label{eq:super_resolution}
y = Ax + \epsilon \ ,
\end{equation}
\vspace{-1mm}
where $A\in \mathbb{R}^M \times \mathbb{R}^N$ represents the point-spread function (PSF) of the electron microscope.
For super-resolution by a factor of $L$, the PSF could be approximated by averaging the values of $L^2$ neighborhood pixels of every $L^2$-th pixel in $x$.
Furthermore, $\epsilon$ is an $M$-dimensional vector 
of i.i.d.\ Gaussian random variables with mean zero and variance $\sigma_w^2$.

We can write the negative log likelihood function as
\vspace{-1mm}
\begin{equation}
l(x) = \frac{ 1 }{ 2 \sigma_w^2 } \| y - A x \|^2 + \frac{ M }{ 2 } \log \left( 2 \pi \sigma_w^2 \right).
\end{equation}
In order to enforce positivity, 
we also modify the negative likelihood function by setting $l(x) = +\infty$ for $x<0$.
Using Eq.~(\ref{eq:F}), the interpolation inversion operator is then given by
\vspace{-1mm}
$$
F( \tilde{x} ; \sigma_{\lambda}) = \argmin_{x \geq 0} \left\{ \frac{1}{2 \sigma_w^2} \|y-Ax\|_2^2 + \frac{1}{2\sigma_{\lambda}^2} \|x - \tilde x\|_2^2 \right\}.
$$

If we let $\sigma_w^2 = 0$, then the inversion operator for super-resolution by a factor of $L$ reduces to the following simple expression
\vspace{-1mm}
\begin{equation}
F(\tilde x; \sigma_{\lambda}) = \left[ \tilde{x} + A^t\left(y - \frac{1}{L^2} A \tilde{x}\right)\right]_+,
\end{equation}
\vspace{-1mm}
where $[\cdot]_+$ enforces positivity.



\subsection{Sparse Interpolation Forward Model}
\label{section:Interpolation}

In this section, we formulate the explicit form of the inversion operator, $F( x, \sigma_\lambda )$,
for the application of sparse interpolation.
More specifically, our objective will be to recover an image $x\in \mathbb{R}^N$
from a noisy and sparsely subsampled version denoted by $y\in \mathbb{R}^M$
where $M \ll N$.
More formally, the forward model for this problem is given by
\vspace{-1mm}
\begin{equation}
\label{eq:sparse_interpolation}
\vspace{-1mm}
y = Ax + \epsilon \ ,
\vspace{-1mm}
\end{equation}
where the sparse sampling matrix, $A\in \mathbb{R}^M \times \mathbb{R}^N$.
Each entry $A_{i,j}$ is either 1 or 0 depending on if the $j^{th}$ pixel is taken
as the $i^{th}$ measurement.
Also, each row of $A$ has exactly one non-zero entry,
and each column of $A$ may either be empty or have one non-zero entry.
Furthermore, $\epsilon$ is an $M$-dimensional vector 
of i.i.d.\ Gaussian random variables with mean zero and variance $\sigma_w^2$.
The log likelihood has the exact form as the sparse interpolation case.

Like in the super-resolution case, if we let $\sigma_w^2 = 0$, then the inversion operator, $F$, reduces to the following explicit expression
\vspace{-1mm}
\begin{equation}
 F(\tilde x; \sigma_{\lambda}) = \left[ \tilde{x} + A^t\left(y - A \tilde{x}\right)\right]_+.
\end{equation}
where $[\cdot]_+$ enforces positivity, 
forcing the interpolation to take on the measured
values at the sample points.



\section{Results}
\label{section:Results}

In this section, we demonstrate the value of our MDF algorithm on three different datasets, all acquired on real electron microscopes. 
We compare our super-resolution reconstructions against state-of-the-art super-resolution algorithms like the single-image super-resolution (SISR) algorithm from Technion \cite{zeyde2010single}, 
and show that fusing multi-resolution data is a powerful framework to form high-quality high-resolution images -- at a fraction of the cost, time, and beam dosage compared to conventional methods.

\subsection{Datasets}

The strength of our experiments lies in the fact that all our test datasets were acquired on real electron microscopes.
As opposed to a post-processing technique, our MDF algorithm is a computational electron microscopy method that combines innovative data acquisition with novel reconstruction algorithms.

High Resolution Transmission Electron Microscopy (HR-TEM) of gold nanorods was performed on an aberration-corrected FEI Titan operating at 300 kV \cite{park2013growth}. 
Images were recorded on a 2k by 2k Gatan Ultrascan CCD at electron optical magnifications ranging from 380 kX to 640kX.
The gold atoms image (Fig.~\ref{fig:gold-atoms}) is a magnified region of edges of these gold nanorods. 

Scanning Electron Microscopy (SEM) of a surface crack in the shell of the mollusk, Hinea brasiliana \cite{deheyn2010bioluminescent} (Fig.~\ref{fig:crystal_crack}) was done on a FEI XL30 at 5 kV accelerating voltage. 

For the sparse interpolation experiment, we use a TEM image of iridovirus assemblies \cite{juhl2006assembly} (Fig.~\ref{fig:iridovirus}), which were cast onto amorphous carbon support films and imaged using a Phillips CM200 Transmission Electron Microscope. 

Note that the Hinea brasiliana image was acquired natively on the FEI Titan microscope at two different resolutions under similar imaging conditions. 
The structure in Fig.~\ref{fig:crystal_crack}(b) and~(c) were acquired at 4$\times$ resolution compared to the structure in Fig.~\ref{fig:crystal_crack}(d) and~(h).
The gold atoms image, on the other hand, was acquired at a single resolution (Fig.~\ref{fig:gold-atoms}(b)). 
We artificially reduced the resolution by 4x, 8x, and 16x 
(see Figs.~\ref{fig:gold-atoms}(c), \ref{fig:gold-atoms}(g), and \ref{fig:gold-atoms}(k), respectively).


\subsection{Experiments}

We apply our MDF algorithm to achieve 4x, 8x, and 16x resolution synthesis results on the atomic-resolution TEM image of gold atoms (Fig.~\ref{fig:gold-atoms}), 4x resolution synthesis on the SEM image of Hinea brasiliana (Fig.~\ref{fig:crystal_crack}), 
and 5\% sparse image interpolation on the TEM image of iridovirus assemblies (Fig.~\ref{fig:iridovirus}).
We show that a variety of denoising algorithms such as doubly-stochastic gradient non-local means (DSG-NLM) \cite{sreehari2016TCI} and library-based non-local means (LB-NLM) can be plugged in as prior models within the P\&P framework to enable data acquisition speedups in EM.

In the super-resolution experiments, we compared the results of our MDF algorithm against cubic interpolation and a state-of-the-art single-image super-resolution (SISR) algorithm from Technion \cite{zeyde2010single}.
The SISR algorithm trains on high-resolution images to learn the microscope model.
To enable fair comparisons, we used the same high-resolution images to train the SISR algorithm as the ones used to create the patch library for our MDF algorithm.
Our MDF algorithm runs significantly faster than the SISR algorithm because the SISR algorithm must be trained specifically for the datasets we use\footnote{Running SISR with their pre-trained dictionaries resulted in higher RMSE.}. 
As an example, the MDF algorithm takes about 4 minutes to run to convergence on the gold atoms dataset presented here, while the SISR algorithm takes $\sim$6 hours to train and about a minute to run. 

In the sparse image interpolation experiment, we compared the result of our MDF algorithm against DSG-NLM and Shepard interpolation.\footnote{In the sparse interpolation experiment, we could not compare against the SISR algorithm since it is not designed for sparse interpolation / inpainting problems.}

To implement the LB-NLM, we built the patch-library by extracting patches from the ``library images'' (see Figs.~\ref{fig:high_res_gold_atoms}, \ref{fig:high_res_crystal}, and \ref{fig:iridovirus_library}).
We did not add noise to the measurements, and therefore set $\sigma_w = 0$. 
As stated earlier, the converged results of P\&P do not depend on the choice of $\sigma_{\lambda}^2$;
however, using the described procedure, we set $\sigma_{\lambda}^2 = 64$ for sparse interpolation, $\sigma_{\lambda}^2 = 55$ for super-resolution of hinea brasiliana, and $\sigma_{\lambda}^2 = 72$ for super-resolution of gold atoms.
The only free parameter for P\&P reconstruction is then the unit-less parameter 
$\beta$,
which we selected to minimize the mean squared error of the reconstruction compared to the ground truth (see Table~\ref{table:parameters}).
For all experiments, we present the P\&P residual convergence resulting from using different priors (see Tables~\ref{table:primal_residues}).
The normalized residue \cite[p. 18]{boyd2011distributed}, $r^{(k)}$ is given by
\begin{eqnarray}
r^{(k)} = \displaystyle\frac{\| \hat{x}^{(k)} - \hat{v}^{(k)} \|_2}{\| \hat{x}^{(\infty)} \|_2} \,
\end{eqnarray}
where $\hat{x}^{(k)}$ and $\hat{v}^{(k)}$ are the values of $\hat{x}$ and $\hat{v}$ respectively after the $k$-th iteration of the P\&P algorithm, respectively, and $\hat{x}^{(\infty)}$ the final value of the reconstruction, $\hat{x}$.



%%%%%       Super-resolution result      %%%%%%

% Super-resolution RMSE table
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|ccc|}
\hline
\multicolumn{4}{ |c| }{\textbf{RMS Error of the Super-Resolution Experiments}} \\
\hline\hline
\textbf{Dataset / } & \textbf{Cubic} & \textbf{SISR} & \textbf{MDF} \\
\textbf{resolution synthesized} & & & \\
\hline\hline
Hinea brasiliana / 4x & 10.33\% & 6.14\% & \textbf{4.10\%} \\
\hline
Gold atoms / 4x & 16.12\% & 11.73\% & \textbf{7.87\%} \\
\hline
Gold atoms / 8x & 39.36\% & 32.58\% & \textbf{12.65\%} \\
\hline
Gold atoms / 16x & 45.71\% & 38.11\% & \textbf{20.89\%} \\
\hline
\end{tabular}
\end{center}
\vspace{-2mm}
\caption{RMSE between the super-resolution interpolated image and the high-resolution ground truth.}
\label{table:super-resolution_error}
\end{table}

\vspace{-2mm}

% Sparse interpolation RMSE table
\begin{table}[H]
\begin{center}
\begin{tabular}{|l|ccc|}
\hline
\multicolumn{4}{ |c| }{\textbf{RMS Error of the Sparse Interpolation Experiment}} \\
\hline\hline
\textbf{Experiment} & \textbf{Shepard} & \textbf{DSG-NLM} & \textbf{MDF} \\
\hline\hline
Sparse interpolation  & 13.10\% & 10.64\% & \textbf{9.71\%} \\
\hline
\end{tabular}
\end{center}
\vspace{-2mm}
\caption{RMSE between the interpolated image and the ground truth.}
\label{table:interpolation_error}
\end{table}


% Convergence table
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|cc|}
\hline
\multicolumn{3}{ |c| }{\textbf{Convergence Error of P\&P}} \\
\hline\hline
\textbf{Experiment} & \textbf{DSG-NLM} & \textbf{MDF} \\
\hline\hline
Sparse interpolation & \textbf{$4.66\times 10^{-8} \%$} & \textbf{$8.98\times 10^{-9} \%$} \\
\hline
Super-resolution & -- & \textbf{$5.91\times 10^{-7} \%$} \\
(hinea brasiliana) & & \\
\hline
Super-resolution & -- & \textbf{$6.09\times 10^{-7} \%$} \\
(gold atoms) & & \\
\hline
\end{tabular}
\end{center}
\vspace{-2mm}
\caption{Convergence error of the P\&P algorithm}
\label{table:primal_residues}
\end{table}


% Parameter table
\begin{table}[htpb!]
\begin{center}
\begin{tabular}{|l|cc|}
\hline
\multicolumn{3}{ |c| }{\textbf{Regularization Parameter, $\beta$}} \\
\hline\hline
\textbf{Experiment} & \textbf{DSG-NLM} & \textbf{MDF} \\
\hline\hline
Sparse interpolation  & 0.39 & 0.42 \\
\hline
Super-resolution & -- & 0.51 \\
(hinea brasiliana) & & \\
\hline
Super-resolution & -- & 0.36 \\
(gold atoms) & & \\
\hline
\end{tabular}
\end{center}
\vspace{-2mm}
\caption{Regularization parameter, $\beta$}
\label{table:parameters}
\end{table}



\begin{figure*}[htbp!]
\centering
\vspace{3mm}
\includegraphics[width=0.235\textwidth]{figs/blank}
~
\subfigure[A portion of the library image]{%
\label{fig:high_res_gold_atoms}
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/Library}}
~
\subfigure[Ground truth]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/Ground_Truth}}
~
\includegraphics[width=0.235\textwidth]{figs/blank}
~


\subfigure[Low-resolution input]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/LR4x}}
~
\subfigure[4x cubic interpolation]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/4_Cubic}}
~
\subfigure[4x SISR]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/4_Elad}}
~
\subfigure[4x MDF (proposed algorithm)]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/4_LBNLM}}
~


\subfigure[Low-resolution input]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/LR8x}}
~
\subfigure[8x cubic interpolation]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/8_cubic}}
~
\subfigure[8x SISR]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/8_Elad}}
~
\subfigure[8x MDF (proposed algorithm)]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/8_LBNLM}}
~


\subfigure[Low-resolution input]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/LR16x}}
~
\subfigure[16x cubic interpolation]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/16_cubic}}
~
\subfigure[16x SISR]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/16_Elad}}
~
\subfigure[16x MDF (proposed algorithm)]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Gold_atoms/16_LBNLM}}

\caption{4x, 8x, and 16x super-resolution of an atomic-resolution TEM image of gold atoms on a carbon substrate -- zoomed in to show details. Subfigures (c), (g), and (k) were obtained by artificially reducing the resolution of the ground truth image (b), by 4x, 8x, and 16x, respectively. These low-resolution images have been rendered by pixel replication to match the size of the ground truth image. Our MDF algorithm resolves the structure of the gold atoms in all of the cases (see (f), (j), and (n)), even when the other methods struggle (see (h), (i), (l), and (m)).}
\label{fig:gold-atoms}
\end{figure*}


% crystal crack

\begin{figure*}[htpb!]
\centering

\includegraphics[width=0.1\textwidth]{figs/blank}
~
\subfigure[A portion of the library image]{%
\label{fig:high_res_crystal}
\includegraphics[width=0.235\textwidth]{figs/Super_resolution/High_res_image_1}}
~
\subfigure[Ground truth]{%
\includegraphics[width=0.235\textwidth]{figs/Super_resolution/high_res_uncropped}}
~
\subfigure[Ground truth (zoomed)]{%
\includegraphics[width=0.235\textwidth]{figs/Super_resolution/high_res_uncropped_zoomed}}
~
\includegraphics[width=0.1\textwidth]{figs/blank}
~
\subfigure[Low-resolution input]{%
\includegraphics[width=0.235\textwidth]{figs/Super_resolution/Crystal_LR4x}}
~
\subfigure[4x cubic interpolation]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Crystal/bicubic}}
~
\subfigure[4x SISR]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Crystal/Elad}}
~
\subfigure[4x MDF (proposed algorithm)]{%
\frame{\includegraphics[width=0.235\textwidth]{figs/Super_resolution/4x_LB_NLM}}}
~
\subfigure[Low-resolution input (zoomed)]{%
\includegraphics[width=0.235\textwidth]{figs/Super_resolution/Crystal_LR4x_zoomed}}
~
\subfigure[4x cubic interpolation (zoomed)]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Crystal/bicubic_zoomed}}
~
\subfigure[4x SISR (zoomed)]{%
\includegraphics[width=0.235\textwidth]{figs/SP_Letters_results/Crystal/Elad_zoomed}}
~
\subfigure[4x MDF (zoomed)]{%
\includegraphics[width=0.235\textwidth]{figs/Super_resolution/4x_LB_NLM_zoomed}}


\caption{4x super-resolution of an SEM image of surface crack in the shell of the marine mollusk \textit{Hinea brasiliana} -- zoomed in to show details. The SEM image in (b) was acquired at 4$\times$ resolution compared to the image in (d), but under similar imaging conditions. Our MDF results in (g) and (k) show the intricate textures and clear edge features that are visually consistent with the ground truth (b). Subfigures (i) and (j) are zoomed in from (e) and (f) respectively. In (i), we see that the cubic interpolation leads to an overly smoothed interpolation, while we see in (j) that the SISR algorithm produces block artifacts.}
\label{fig:crystal_crack}
\end{figure*}




% iridovirus

\begin{figure*}[htbp!]
\centering
\includegraphics[width=0.235\textwidth]{figs/blank}
\subfigure[Library image]{%
\label{fig:iridovirus_library}
\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/library}}
~
\subfigure[Ground truth]{%
\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/ground_truth_zoomed}}
~
{%
\includegraphics[width=0.235\textwidth]{figs/blank}}
%~
%\subfigure[Ground truth]{%
%\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/ground_truth}}
%~
%\subfigure[Shepard interpolation]{%
%\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/5_Shepard}}
%~
%\subfigure[DSG-NLM interpolation]{%
%\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/5_DSG_NLM}}
%~
%\subfigure[MDF interpolation]{%
%\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/5_LB_NLM}}
%~
\subfigure[$5\%$ sampling of (b)]{%
\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/5_sampling}}
~
\subfigure[Shepard interpolation]{%
\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/5_Shepard_zoomed}}
~
\subfigure[DSG-NLM interpolation]{%
\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/5_DSG_NLM_zoomed}}
~
\subfigure[MDF interpolation (proposed algorithm)]{%
\includegraphics[width=0.235\textwidth]{figs/Sparse_interpolation/iridovirus/5_LB_NLM_zoomed}}


\caption{Interpolation of a TEM image of iridovirus assemblies on a carbon substrate; (c) shows the 5\% randomly sampled image that serves as the input to all the interpolation methods; (f) shows the texture synthesized by our MDF algorithm, which is visually more accurate compared to that generated by DSG-NLM in (e) and Shepard's interpolation in (d). In addition, the MDF interpolation results in the least mean squared error of all the methods.}
\label{fig:iridovirus}
\end{figure*}


Our MDF reconstructions result in 15x to 228x data acquisition speedup across our datasets. 
The speedup factors are computed as the ratio of the number of pixels in the reconstructed image to the number of pixels measured. In addition to specifying the speedup factors, we specify the size of our high-resolution library relative to the size of the low-resolution image acquired through the quantity,
\begin{equation}
\rho = \frac{\text{\# of high-resolution pixels}}{\text{\# of total pixels}}.
\end{equation}
Table~\ref{table:speedup_factors} gives the value of $\rho$ and the speedup factors for each of our experiments.
\begin{table}[htpb!]
\begin{center}
\begin{tabular}{|l|cc|}
\hline
\multicolumn{3}{ |c| }{\textbf{Data Acquisition Speedup}} \\
\hline\hline
\textbf{Experiment} & \textbf{$\rho$} & \textbf{Speedup factor} \\
\hline\hline
Super-resolution & 6.11\% & 15x \\
(hinea brasiliana / 4x) & & \\
\hline
Super-resolution & 0.76\% & 15.87x \\
(gold atoms / 4x) & & \\
\hline
Super-resolution & 2.96\% & 62.1x \\
(gold atoms / 8x) & & \\
\hline
Super-resolution & 10.88\% & 228.14x \\
(gold atoms / 16x) & & \\
\hline
Sparse interpolation  & 8.74\% & 18.25x \\
(iridovirus)  & &  \\
\hline
\end{tabular}
\end{center}
\vspace{-2mm}
\caption{Data acquisition speedup achieved by our MDF algorithm. The ratio of the high-resolution pixels measured to the low-resolution pixels measured is given by $\rho$.}
\label{table:speedup_factors}
\end{table}

Importantly, the MDF reconstructions are clearer than Shepard and cubic interpolations, despite the high speedup factors achieved. 
Also, MDF results in the least mean squared error (see Tables~\ref{table:super-resolution_error} and \ref{table:interpolation_error}).
%, and also makes P\&P converge. 
The MDF algorithm also substantially reduces jaggies and produces better textures and features compared to Technion's SISR algorithm as well as cubic and Shepard interpolations.


\section{Conclusion}
\label{section:Conclusion}

Traditional EM imaging based on homogeneous raster-order scanning severely limits the volume of high-resolution data that can be collected, 
and presents a fundamental limitation to understanding many important physical processes.

In this paper, we introduced a novel computational electron microscopy imaging method based on multi-resolution data fusion (MDF) that combines innovative data acquisition with novel algorithmic techniques to dramatically improve the resolution/volume/speed/dosage trade-off as compared to traditional EM imaging methods. 
High-resolution measurements taken over a small field-of-view are used to create a material-specific probabilistic model in the form of a patch-library that is used to dramatically increase resolution. 
We introduced a Bayesian framework for the fusion of high and low-resolution data without the need for training. 
We outlined a library-based non-local means (LB-NLM) algorithm that uses typical high-resolution patches, 
and we used it as a prior model within the \textit{plug-and-play priors} framework to produce visually true textures and edge features in the interpolations, while significantly reducing mean squared error. 
Finally, we presented 4x, 8x, and 16x super-resolution and 5\% sparse image interpolation results demonstrating data acquisition speedups of 15x to 228x on various datasets, while substantially maintaining image quality. 
Our MDF algorithm greatly increases acquisition speed and reduces the electron beam dosage.
We demonstrated the power of our method on real electron microscope images and compared our results against Technion's state-of-the-art single-image super-resolution (SISR) algorithm.
In our experiments, we found our MDF algorithm to consistently produce clearer, sharper image reconstructions with visibly truer textures and lower mean squared error compared to the SISR, cubic, and Shepard interpolations.

In summary, our MDF computational EM method enables high-resolution EM data to be collected at a fraction of the time as conventional methods, while maintaining high image quality -- offering an \textit{integrated imaging} solution to a grand challenge problem in electron microscopy.

{\small
\bibliographystyle{ieee}
\bibliography{References}
}

\end{document}

bare_adv.tex

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% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/


%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
% which rewrites many portions of the LaTeX2e float routines. It may not work
% with other packages that modify the LaTeX2e float routines. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
% Do not use the stfloats baselinefloat ability as IEEE does not allow
% \baselineskip to stretch. Authors submitting work to the IEEE should note
% that IEEE rarely uses double column equations and that authors should try
% to avoid such use. Do not be tempted to use the cuted.sty or midfloat.sty
% packages (also by Sigitas Tolusis) as IEEE does not format its papers in
% such ways.
% Do not attempt to use stfloats with fixltx2e as they are incompatible.
% Instead, use Morten Hogholm'a dblfloatfix which combines the features
% of both fixltx2e and stfloats:
%
% \usepackage{dblfloatfix}
% The latest version can be found at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/dblfloatfix/


%\ifCLASSOPTIONcaptionsoff
%  \usepackage[nomarkers]{endfloat}
% \let\MYoriglatexcaption\caption
% \renewcommand{\caption}[2][\relax]{\MYoriglatexcaption[#2]{#2}}
%\fi
% endfloat.sty was written by James Darrell McCauley, Jeff Goldberg and 
% Axel Sommerfeldt. This package may be useful when used in conjunction with 
% IEEEtran.cls'  captionsoff option. Some IEEE journals/societies require that
% submissions have lists of figures/tables at the end of the paper and that
% figures/tables without any captions are placed on a page by themselves at
% the end of the document. If needed, the draftcls IEEEtran class option or
% \CLASSINPUTbaselinestretch interface can be used to increase the line
% spacing as well. Be sure and use the nomarkers option of endfloat to
% prevent endfloat from "marking" where the figures would have been placed
% in the text. The two hack lines of code above are a slight modification of
% that suggested by in the endfloat docs (section 8.4.1) to ensure that
% the full captions always appear in the list of figures/tables - even if
% the user used the short optional argument of \caption[]{}.
% IEEE papers do not typically make use of \caption[]'s optional argument,
% so this should not be an issue. A similar trick can be used to disable
% captions of packages such as subfig.sty that lack options to turn off
% the subcaptions:
% For subfig.sty:
% \let\MYorigsubfloat\subfloat
% \renewcommand{\subfloat}[2][\relax]{\MYorigsubfloat[]{#2}}
% However, the above trick will not work if both optional arguments of
% the \subfloat command are used. Furthermore, there needs to be a
% description of each subfigure *somewhere* and endfloat does not add
% subfigure captions to its list of figures. Thus, the best approach is to
% avoid the use of subfigure captions (many IEEE journals avoid them anyway)
% and instead reference/explain all the subfigures within the main caption.
% The latest version of endfloat.sty and its documentation can obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/endfloat/
%
% The IEEEtran \ifCLASSOPTIONcaptionsoff conditional can also be used
% later in the document, say, to conditionally put the References on a 
% page by themselves.





% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/url/
% Basically, \url{my_url_here}.


% NOTE: PDF thumbnail features are not required in IEEE papers
%       and their use requires extra complexity and work.
%\ifCLASSINFOpdf
%  \usepackage[pdftex]{thumbpdf}
%\else
%  \usepackage[dvips]{thumbpdf}
%\fi
% thumbpdf.sty and its companion Perl utility were written by Heiko Oberdiek.
% It allows the user a way to produce PDF documents that contain fancy
% thumbnail images of each of the pages (which tools like acrobat reader can
% utilize). This is possible even when using dvi->ps->pdf workflow if the
% correct thumbpdf driver options are used. thumbpdf.sty incorporates the
% file containing the PDF thumbnail information (filename.tpm is used with
% dvips, filename.tpt is used with pdftex, where filename is the base name of
% your tex document) into the final ps or pdf output document. An external
% utility, the thumbpdf *Perl script* is needed to make these .tpm or .tpt
% thumbnail files from a .ps or .pdf version of the document (which obviously
% does not yet contain pdf thumbnails). Thus, one does a:
% 
% thumbpdf filename.pdf 
%
% to make a filename.tpt, and:
%
% thumbpdf --mode dvips filename.ps
%
% to make a filename.tpm which will then be loaded into the document by
% thumbpdf.sty the NEXT time the document is compiled (by pdflatex or
% latex->dvips->ps2pdf). Users must be careful to regenerate the .tpt and/or
% .tpm files if the main document changes and then to recompile the
% document to incorporate the revised thumbnails to ensure that thumbnails
% match the actual pages. It is easy to forget to do this!
% 
% Unix systems come with a Perl interpreter. However, MS Windows users
% will usually have to install a Perl interpreter so that the thumbpdf
% script can be run. The Ghostscript PS/PDF interpreter is also required.
% See the thumbpdf docs for details. The latest version and documentation
% can be obtained at.
% http://www.ctan.org/tex-archive/support/thumbpdf/


% NOTE: PDF hyperlink and bookmark features are not required in IEEE
%       papers and their use requires extra complexity and work.
% *** IF USING HYPERREF BE SURE AND CHANGE THE EXAMPLE PDF ***
% *** TITLE/SUBJECT/AUTHOR/KEYWORDS INFO BELOW!!           ***
\newcommand\MYhyperrefoptions{bookmarks=true,bookmarksnumbered=true,
pdfpagemode={UseOutlines},plainpages=false,pdfpagelabels=true,
colorlinks=true,linkcolor={black},citecolor={black},urlcolor={black},
pdftitle={Bare Demo of IEEEtran.cls for Computer Society Journals},%<!CHANGE!
pdfsubject={Typesetting},%<!CHANGE!
pdfauthor={Michael D. Shell},%<!CHANGE!
pdfkeywords={Computer Society, IEEEtran, journal, LaTeX, paper,
             template}}%<^!CHANGE!
%\ifCLASSINFOpdf
%\usepackage[\MYhyperrefoptions,pdftex]{hyperref}
%\else
%\usepackage[\MYhyperrefoptions,breaklinks=true,dvips]{hyperref}
%\usepackage{breakurl}
%\fi
% One significant drawback of using hyperref under DVI output is that the
% LaTeX compiler cannot break URLs across lines or pages as can be done
% under pdfLaTeX's PDF output via the hyperref pdftex driver. This is
% probably the single most important capability distinction between the
% DVI and PDF output. Perhaps surprisingly, all the other PDF features
% (PDF bookmarks, thumbnails, etc.) can be preserved in
% .tex->.dvi->.ps->.pdf workflow if the respective packages/scripts are
% loaded/invoked with the correct driver options (dvips, etc.). 
% As most IEEE papers use URLs sparingly (mainly in the references), this
% may not be as big an issue as with other publications.
%
% That said, Vilar Camara Neto created his breakurl.sty package which
% permits hyperref to easily break URLs even in dvi mode.
% Note that breakurl, unlike most other packages, must be loaded
% AFTER hyperref. The latest version of breakurl and its documentation can
% be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/breakurl/
% breakurl.sty is not for use under pdflatex pdf mode.
%
% The advanced features offer by hyperref.sty are not required for IEEE
% submission, so users should weigh these features against the added
% complexity of use.
% The package options above demonstrate how to enable PDF bookmarks
% (a type of table of contents viewable in Acrobat Reader) as well as
% PDF document information (title, subject, author and keywords) that is
% viewable in Acrobat reader's Document_Properties menu. PDF document
% information is also used extensively to automate the cataloging of PDF
% documents. The above set of options ensures that hyperlinks will not be
% colored in the text and thus will not be visible in the printed page,
% but will be active on "mouse over". USING COLORS OR OTHER HIGHLIGHTING
% OF HYPERLINKS CAN RESULT IN DOCUMENT REJECTION BY THE IEEE, especially if
% these appear on the "printed" page. IF IN DOUBT, ASK THE RELEVANT
% SUBMISSION EDITOR. You may need to add the option hypertexnames=false if
% you used duplicate equation numbers, etc., but this should not be needed
% in normal IEEE work.
% The latest version of hyperref and its documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/hyperref/





% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )


% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
%
% paper title
% Titles are generally capitalized except for words such as a, an, and, as,
% at, but, by, for, in, nor, of, on, or, the, to and up, which are usually
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Bare Advanced Demo of IEEEtran.cls\\ for Computer Society Journals}
%
%
% author names and IEEE memberships
% note positions of commas and nonbreaking spaces ( ~ ) LaTeX will not break
% a structure at a ~ so this keeps an author's name from being broken across
% two lines.
% use \thanks{} to gain access to the first footnote area
% a separate \thanks must be used for each paragraph as LaTeX2e's \thanks
% was not built to handle multiple paragraphs
%
%
%\IEEEcompsocitemizethanks is a special \thanks that produces the bulleted
% lists the Computer Society journals use for "first footnote" author
% affiliations. Use \IEEEcompsocthanksitem which works much like \item
% for each affiliation group. When not in compsoc mode,
% \IEEEcompsocitemizethanks becomes like \thanks and
% \IEEEcompsocthanksitem becomes a line break with idention. This
% facilitates dual compilation, although admittedly the differences in the
% desired content of \author between the different types of papers makes a
% one-size-fits-all approach a daunting prospect. For instance, compsoc 
% journal papers have the author affiliations above the "Manuscript
% received ..."  text while in non-compsoc journals this is reversed. Sigh.

\author{Michael~Shell,~\IEEEmembership{Member,~IEEE,}
        John~Doe,~\IEEEmembership{Fellow,~OSA,}
        and~Jane~Doe,~\IEEEmembership{Life~Fellow,~IEEE}% <-this % stops a space
\IEEEcompsocitemizethanks{\IEEEcompsocthanksitem M. Shell is with the Department
of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta,
GA, 30332.\protect\\
% note need leading \protect in front of \\ to get a newline within \thanks as
% \\ is fragile and will error, could use \hfil\break instead.
E-mail: see http://www.michaelshell.org/contact.html
\IEEEcompsocthanksitem J. Doe and J. Doe are with Anonymous University.}% <-this % stops a space
\thanks{Manuscript received April 19, 2005; revised September 17, 2014.}}

% note the % following the last \IEEEmembership and also \thanks - 
% these prevent an unwanted space from occurring between the last author name
% and the end of the author line. i.e., if you had this:
% 
% \author{....lastname \thanks{...} \thanks{...} }
%                     ^------------^------------^----Do not want these spaces!
%
% a space would be appended to the last name and could cause every name on that
% line to be shifted left slightly. This is one of those "LaTeX things". For
% instance, "\textbf{A} \textbf{B}" will typeset as "A B" not "AB". To get
% "AB" then you have to do: "\textbf{A}\textbf{B}"
% \thanks is no different in this regard, so shield the last } of each \thanks
% that ends a line with a % and do not let a space in before the next \thanks.
% Spaces after \IEEEmembership other than the last one are OK (and needed) as
% you are supposed to have spaces between the names. For what it is worth,
% this is a minor point as most people would not even notice if the said evil
% space somehow managed to creep in.



% The paper headers
\markboth{Journal of \LaTeX\ Class Files,~Vol.~13, No.~9, September~2014}%
{Shell \MakeLowercase{\textit{et al.}}: Bare Advanced Demo of IEEEtran.cls for Journals}
% The only time the second header will appear is for the odd numbered pages
% after the title page when using the twoside option.
% 
% *** Note that you probably will NOT want to include the author's ***
% *** name in the headers of peer review papers.                   ***
% You can use \ifCLASSOPTIONpeerreview for conditional compilation here if
% you desire.



% The publisher's ID mark at the bottom of the page is less important with
% Computer Society journal papers as those publications place the marks
% outside of the main text columns and, therefore, unlike regular IEEE
% journals, the available text space is not reduced by their presence.
% If you want to put a publisher's ID mark on the page you can do it like
% this:
%\IEEEpubid{0000--0000/00\$00.00~\copyright~2014 IEEE}
% or like this to get the Computer Society new two part style.
%\IEEEpubid{\makebox[\columnwidth]{\hfill 0000--0000/00/\$00.00~\copyright~2014 IEEE}%
%\hspace{\columnsep}\makebox[\columnwidth]{Published by the IEEE Computer Society\hfill}}
% Remember, if you use this you must call \IEEEpubidadjcol in the second
% column for its text to clear the IEEEpubid mark (Computer Society journal
% papers don't need this extra clearance.)



% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}



% for Computer Society papers, we must declare the abstract and index terms
% PRIOR to the title within the \IEEEtitleabstractindextext IEEEtran
% command as these need to go into the title area created by \maketitle.
% As a general rule, do not put math, special symbols or citations
% in the abstract or keywords.
\IEEEtitleabstractindextext{%
\begin{abstract}
The abstract goes here.
\end{abstract}

% Note that keywords are not normally used for peerreview papers.
\begin{IEEEkeywords}
Computer Society, IEEEtran, journal, \LaTeX, paper, template.
\end{IEEEkeywords}}


% make the title area
\maketitle


% To allow for easy dual compilation without having to reenter the
% abstract/keywords data, the \IEEEtitleabstractindextext text will
% not be used in maketitle, but will appear (i.e., to be "transported")
% here as \IEEEdisplaynontitleabstractindextext when compsoc mode
% is not selected <OR> if conference mode is selected - because compsoc
% conference papers position the abstract like regular (non-compsoc)
% papers do!
\IEEEdisplaynontitleabstractindextext
% \IEEEdisplaynontitleabstractindextext has no effect when using
% compsoc under a non-conference mode.


% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle


\ifCLASSOPTIONcompsoc
\IEEEraisesectionheading{\section{Introduction}\label{sec:introduction}}
\else
\section{Introduction}
\label{sec:introduction}
\fi
% Computer Society journal (but not conference!) papers do something unusual
% with the very first section heading (almost always called "Introduction").
% They place it ABOVE the main text! IEEEtran.cls does not automatically do
% this for you, but you can achieve this effect with the provided
% \IEEEraisesectionheading{} command. Note the need to keep any \label that
% is to refer to the section immediately after \section in the above as
% \IEEEraisesectionheading puts \section within a raised box.




% The very first letter is a 2 line initial drop letter followed
% by the rest of the first word in caps (small caps for compsoc).
% 
% form to use if the first word consists of a single letter:
% \IEEEPARstart{A}{demo} file is ....
% 
% form to use if you need the single drop letter followed by
% normal text (unknown if ever used by IEEE):
% \IEEEPARstart{A}{}demo file is ....
% 
% Some journals put the first two words in caps:
% \IEEEPARstart{T}{his demo} file is ....
% 
% Here we have the typical use of a "T" for an initial drop letter
% and "HIS" in caps to complete the first word.
\IEEEPARstart{T}{his} demo file is intended to serve as a ``starter file''
for IEEE Computer Society journal papers produced under \LaTeX\ using
IEEEtran.cls version 1.8a and later.
% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)
I wish you the best of success.

\hfill mds
 
\hfill September 17, 2014

\subsection{Subsection Heading Here}
Subsection text here.

% needed in second column of first page if using \IEEEpubid
%\IEEEpubidadjcol

\subsubsection{Subsubsection Heading Here}
Subsubsection text here.


% An example of a floating figure using the graphicx package.
% Note that \label must occur AFTER (or within) \caption.
% For figures, \caption should occur after the \includegraphics.
% Note that IEEEtran v1.7 and later has special internal code that
% is designed to preserve the operation of \label within \caption
% even when the captionsoff option is in effect. However, because
% of issues like this, it may be the safest practice to put all your
% \label just after \caption rather than within \caption{}.
%
% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
% option should be used if it is desired that the figures are to be
% displayed while in draft mode.
%
%\begin{figure}[!t]
%\centering
%\includegraphics[width=2.5in]{myfigure}
% where an .eps filename suffix will be assumed under latex, 
% and a .pdf suffix will be assumed for pdflatex; or what has been declared
% via \DeclareGraphicsExtensions.
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure}

% Note that IEEE typically puts floats only at the top, even when this
% results in a large percentage of a column being occupied by floats.
% However, the Computer Society has been known to put floats at the bottom.


% An example of a double column floating figure using two subfigures.
% (The subfig.sty package must be loaded for this to work.)
% The subfigure \label commands are set within each subfloat command,
% and the \label for the overall figure must come after \caption.
% \hfil is used as a separator to get equal spacing.
% Watch out that the combined width of all the subfigures on a 
% line do not exceed the text width or a line break will occur.
%
%\begin{figure*}[!t]
%\centering
%\subfloat[Case I]{\includegraphics[width=2.5in]{box}%
%\label{fig_first_case}}
%\hfil
%\subfloat[Case II]{\includegraphics[width=2.5in]{box}%
%\label{fig_second_case}}
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure*}
%
% Note that often IEEE papers with subfigures do not employ subfigure
% captions (using the optional argument to \subfloat[]), but instead will
% reference/describe all of them (a), (b), etc., within the main caption.
% Be aware that for subfig.sty to generate the (a), (b), etc., subfigure
% labels, the optional argument to \subfloat must be present. If a
% subcaption is not desired, just leave its contents blank,
% e.g., \subfloat[].


% An example of a floating table. Note that, for IEEE style tables, the
% \caption command should come BEFORE the table and, given that table
% captions serve much like titles, are usually capitalized except for words
% such as a, an, and, as, at, but, by, for, in, nor, of, on, or, the, to
% and up, which are usually not capitalized unless they are the first or
% last word of the caption. Table text will default to \footnotesize as
% IEEE normally uses this smaller font for tables.
% The \label must come after \caption as always.
%
%\begin{table}[!t]
%% increase table row spacing, adjust to taste
%\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of
% \extrarowheight as needed to properly center the text within the cells
%\caption{An Example of a Table}
%\label{table_example}
%\centering
%% Some packages, such as MDW tools, offer better commands for making tables
%% than the plain LaTeX2e tabular which is used here.
%\begin{tabular}{|c||c|}
%\hline
%One & Two\\
%\hline
%Three & Four\\
%\hline
%\end{tabular}
%\end{table}


% Note that the IEEE does not put floats in the very first column
% - or typically anywhere on the first page for that matter. Also,
% in-text middle ("here") positioning is typically not used, but it
% is allowed and encouraged for Computer Society conferences (but
% not Computer Society journals). Most IEEE journals/conferences use
% top floats exclusively. 
% Note that, LaTeX2e, unlike IEEE journals/conferences, places
% footnotes above bottom floats. This can be corrected via the
% \fnbelowfloat command of the stfloats package.




\section{Conclusion}
The conclusion goes here.





% if have a single appendix:
%\appendix[Proof of the Zonklar Equations]
% or
%\appendix  % for no appendix heading
% do not use \section anymore after \appendix, only \section*
% is possibly needed

% use appendices with more than one appendix
% then use \section to start each appendix
% you must declare a \section before using any
% \subsection or using \label (\appendices by itself
% starts a section numbered zero.)
%


\appendices
\section{Proof of the First Zonklar Equation}
Appendix one text goes here.

% you can choose not to have a title for an appendix
% if you want by leaving the argument blank
\section{}
Appendix two text goes here.


% use section* for acknowledgment
\ifCLASSOPTIONcompsoc
  % The Computer Society usually uses the plural form
  \section*{Acknowledgments}
\else
  % regular IEEE prefers the singular form
  \section*{Acknowledgment}
\fi


The authors would like to thank...


% Can use something like this to put references on a page
% by themselves when using endfloat and the captionsoff option.
\ifCLASSOPTIONcaptionsoff
  \newpage
\fi



% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
\begin{thebibliography}{1}

\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to {\LaTeX}}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}

% biography section
% 
% If you have an EPS/PDF photo (graphicx package needed) extra braces are
% needed around the contents of the optional argument to biography to prevent
% the LaTeX parser from getting confused when it sees the complicated
% \includegraphics command within an optional argument. (You could create
% your own custom macro containing the \includegraphics command to make things
% simpler here.)
%\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
% or if you just want to reserve a space for a photo:

\begin{IEEEbiography}{Michael Shell}
Biography text here.
\end{IEEEbiography}

% if you will not have a photo at all:
\begin{IEEEbiographynophoto}{John Doe}
Biography text here.
\end{IEEEbiographynophoto}

% insert where needed to balance the two columns on the last page with
% biographies
%\newpage

\begin{IEEEbiographynophoto}{Jane Doe}
Biography text here.
\end{IEEEbiographynophoto}

% You can push biographies down or up by placing
% a \vfill before or after them. The appropriate
% use of \vfill depends on what kind of text is
% on the last page and whether or not the columns
% are being equalized.

%\vfill

% Can be used to pull up biographies so that the bottom of the last one
% is flush with the other column.
%\enlargethispage{-5in}



% that's all folks
\end{document}



bare_conf_compsoc.tex

%% bare_conf_compsoc.tex
%% V1.4a
%% 2014/09/17
%% by Michael Shell
%% See:
%% http://www.michaelshell.org/
%% for current contact information.
%%
%% This is a skeleton file demonstrating the use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.8s or later) with an IEEE Computer
%% Society conference paper.
%%
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
%% and
%% http://www.ieee.org/

%%*************************************************************************
%% Legal Notice:
%% This code is offered as-is without any warranty either expressed or
%% implied; without even the implied warranty of MERCHANTABILITY or
%% FITNESS FOR A PARTICULAR PURPOSE! 
%% User assumes all risk.
%% In no event shall IEEE or any contributor to this code be liable for
%% any damages or losses, including, but not limited to, incidental,
%% consequential, or any other damages, resulting from the use or misuse
%% of any information contained here.
%%
%% All comments are the opinions of their respective authors and are not
%% necessarily endorsed by the IEEE.
%%
%% This work is distributed under the LaTeX Project Public License (LPPL)
%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
%% distributed and modified. A copy of the LPPL, version 1.3, is included
%% in the base LaTeX documentation of all distributions of LaTeX released
%% 2003/12/01 or later.
%% Retain all contribution notices and credits.
%% ** Modified files should be clearly indicated as such, including  **
%% ** renaming them and changing author support contact information. **
%%
%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%%                    bare_conf.tex, bare_jrnl.tex, bare_conf_compsoc.tex,
%%                    bare_jrnl_compsoc.tex, bare_jrnl_transmag.tex
%%*************************************************************************


% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices and paper sizes can       ***
% *** trigger bugs that do not appear when using other class files.       ***                          ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/



\documentclass[conference,compsoc]{IEEEtran}
% Some/most Computer Society conferences require the compsoc mode option,
% but others may want the standard conference format.
%
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
% \documentclass[conference,compsoc]{../sty/IEEEtran}





% Some very useful LaTeX packages include:
% (uncomment the ones you want to load)


% *** MISC UTILITY PACKAGES ***
%
%\usepackage{ifpdf}
% Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
% compilation based on whether the output is pdf or dvi.
% usage:
% \ifpdf
%   % pdf code
% \else
%   % dvi code
% \fi
% The latest version of ifpdf.sty can be obtained from:
% http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
% Also, note that IEEEtran.cls V1.7 and later provides a builtin
% \ifCLASSINFOpdf conditional that works the same way.
% When switching from latex to pdflatex and vice-versa, the compiler may
% have to be run twice to clear warning/error messages.






% *** CITATION PACKAGES ***
%
\ifCLASSOPTIONcompsoc
  % IEEE Computer Society needs nocompress option
  % requires cite.sty v4.0 or later (November 2003)
  \usepackage[nocompress]{cite}
\else
  % normal IEEE
  \usepackage{cite}
\fi
% cite.sty was written by Donald Arseneau
% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
% \cite{} output to follow that of IEEE. Loading the cite package will
% result in citation numbers being automatically sorted and properly
% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
% \cite will automatically add leading space, if needed. Use cite.sty's
% noadjust option (cite.sty V3.8 and later) if you want to turn this off
% such as if a citation ever needs to be enclosed in parenthesis.
% cite.sty is already installed on most LaTeX systems. Be sure and use
% version 5.0 (2009-03-20) and later if using hyperref.sty.
% The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
% The documentation is contained in the cite.sty file itself.
%
% Note that some packages require special options to format as the Computer
% Society requires. In particular, Computer Society  papers do not use
% compressed citation ranges as is done in typical IEEE papers
% (e.g., [1]-[4]). Instead, they list every citation separately in order
% (e.g., [1], [2], [3], [4]). To get the latter we need to load the cite
% package with the nocompress option which is supported by cite.sty v4.0
% and later.





% *** GRAPHICS RELATED PACKAGES ***
%
\ifCLASSINFOpdf
  % \usepackage[pdftex]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../pdf/}{../jpeg/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
\else
  % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
  % will default to the driver specified in the system graphics.cfg if no
  % driver is specified.
  % \usepackage[dvips]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../eps/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.eps}
\fi
% graphicx was written by David Carlisle and Sebastian Rahtz. It is
% required if you want graphics, photos, etc. graphicx.sty is already
% installed on most LaTeX systems. The latest version and documentation
% can be obtained at: 
% http://www.ctan.org/tex-archive/macros/latex/required/graphics/
% Another good source of documentation is "Using Imported Graphics in
% LaTeX2e" by Keith Reckdahl which can be found at:
% http://www.ctan.org/tex-archive/info/epslatex/
%
% latex, and pdflatex in dvi mode, support graphics in encapsulated
% postscript (.eps) format. pdflatex in pdf mode supports graphics
% in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
% that all non-photo figures use a vector format (.eps, .pdf, .mps) and
% not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
% which can result in "jaggedy"/blurry rendering of lines and letters as
% well as large increases in file sizes.
%
% You can find documentation about the pdfTeX application at:
% http://www.tug.org/applications/pdftex





% *** MATH PACKAGES ***
%
%\usepackage[cmex10]{amsmath}
% A popular package from the American Mathematical Society that provides
% many useful and powerful commands for dealing with mathematics. If using
% it, be sure to load this package with the cmex10 option to ensure that
% only type 1 fonts will utilized at all point sizes. Without this option,
% it is possible that some math symbols, particularly those within
% footnotes, will be rendered in bitmap form which will result in a
% document that can not be IEEE Xplore compliant!
%
% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
% thus preventing page breaks from occurring within multiline equations. Use:
%\interdisplaylinepenalty=2500
% after loading amsmath to restore such page breaks as IEEEtran.cls normally
% does. amsmath.sty is already installed on most LaTeX systems. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/





% *** SPECIALIZED LIST PACKAGES ***
%
%\usepackage{algorithmic}
% algorithmic.sty was written by Peter Williams and Rogerio Brito.
% This package provides an algorithmic environment fo describing algorithms.
% You can use the algorithmic environment in-text or within a figure
% environment to provide for a floating algorithm. Do NOT use the algorithm
% floating environment provided by algorithm.sty (by the same authors) or
% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
% algorithm float types and packages that provide these will not provide
% correct IEEE style captions. The latest version and documentation of
% algorithmic.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
% There is also a support site at:
% http://algorithms.berlios.de/index.html
% Also of interest may be the (relatively newer and more customizable)
% algorithmicx.sty package by Szasz Janos:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/




% *** ALIGNMENT PACKAGES ***
%
%\usepackage{array}
% Frank Mittelbach's and David Carlisle's array.sty patches and improves
% the standard LaTeX2e array and tabular environments to provide better
% appearance and additional user controls. As the default LaTeX2e table
% generation code is lacking to the point of almost being broken with
% respect to the quality of the end results, all users are strongly
% advised to use an enhanced (at the very least that provided by array.sty)
% set of table tools. array.sty is already installed on most systems. The
% latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/tools/


% IEEEtran contains the IEEEeqnarray family of commands that can be used to
% generate multiline equations as well as matrices, tables, etc., of high
% quality.




% *** SUBFIGURE PACKAGES ***
%\ifCLASSOPTIONcompsoc
%  \usepackage[caption=false,font=footnotesize,labelfont=sf,textfont=sf]{subfig}
%\else
%  \usepackage[caption=false,font=footnotesize]{subfig}
%\fi
% subfig.sty, written by Steven Douglas Cochran, is the modern replacement
% for subfigure.sty, the latter of which is no longer maintained and is
% incompatible with some LaTeX packages including fixltx2e. However,
% subfig.sty requires and automatically loads Axel Sommerfeldt's caption.sty
% which will override IEEEtran.cls' handling of captions and this will result
% in non-IEEE style figure/table captions. To prevent this problem, be sure
% and invoke subfig.sty's "caption=false" package option (available since
% subfig.sty version 1.3, 2005/06/28) as this is will preserve IEEEtran.cls
% handling of captions.
% Note that the Computer Society format requires a sans serif font rather
% than the serif font used in traditional IEEE formatting and thus the need
% to invoke different subfig.sty package options depending on whether
% compsoc mode has been enabled.
%
% The latest version and documentation of subfig.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/




% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/


%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
% which rewrites many portions of the LaTeX2e float routines. It may not work
% with other packages that modify the LaTeX2e float routines. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
% Do not use the stfloats baselinefloat ability as IEEE does not allow
% \baselineskip to stretch. Authors submitting work to the IEEE should note
% that IEEE rarely uses double column equations and that authors should try
% to avoid such use. Do not be tempted to use the cuted.sty or midfloat.sty
% packages (also by Sigitas Tolusis) as IEEE does not format its papers in
% such ways.
% Do not attempt to use stfloats with fixltx2e as they are incompatible.
% Instead, use Morten Hogholm'a dblfloatfix which combines the features
% of both fixltx2e and stfloats:
%
% \usepackage{dblfloatfix}
% The latest version can be found at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/dblfloatfix/




% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/url/
% Basically, \url{my_url_here}.




% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )


% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
%
% paper title
% Titles are generally capitalized except for words such as a, an, and, as,
% at, but, by, for, in, nor, of, on, or, the, to and up, which are usually
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Bare Demo of IEEEtran.cls for Computer Society Conferences}


% author names and affiliations
% use a multiple column layout for up to three different
% affiliations
\author{\IEEEauthorblockN{Michael Shell}
\IEEEauthorblockA{School of Electrical and\\Computer Engineering\\
Georgia Institute of Technology\\
Atlanta, Georgia 30332--0250\\
Email: http://www.michaelshell.org/contact.html}
\and
\IEEEauthorblockN{Homer Simpson}
\IEEEauthorblockA{Twentieth Century Fox\\
Springfield, USA\\
Email: homer@thesimpsons.com}
\and
\IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
\IEEEauthorblockA{Starfleet Academy\\
San Francisco, California 96678-2391\\
Telephone: (800) 555--1212\\
Fax: (888) 555--1212}}

% conference papers do not typically use \thanks and this command
% is locked out in conference mode. If really needed, such as for
% the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
% after \documentclass

% for over three affiliations, or if they all won't fit within the width
% of the page (and note that there is less available width in this regard for
% compsoc conferences compared to traditional conferences), use this
% alternative format:
% 
%\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
%Homer Simpson\IEEEauthorrefmark{2},
%James Kirk\IEEEauthorrefmark{3}, 
%Montgomery Scott\IEEEauthorrefmark{3} and
%Eldon Tyrell\IEEEauthorrefmark{4}}
%\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
%Georgia Institute of Technology,
%Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
%\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
%Email: homer@thesimpsons.com}
%\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
%Telephone: (800) 555--1212, Fax: (888) 555--1212}
%\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}




% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}




% make the title area
\maketitle

% As a general rule, do not put math, special symbols or citations
% in the abstract
\begin{abstract}
The abstract goes here.
\end{abstract}

% no keywords




% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle



\section{Introduction}
% no \IEEEPARstart
This demo file is intended to serve as a ``starter file''
for IEEE conference papers produced under \LaTeX\ using
IEEEtran.cls version 1.8a and later.
% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)
I wish you the best of success.

\hfill mds
 
\hfill September 17, 2014

\subsection{Subsection Heading Here}
Subsection text here.


\subsubsection{Subsubsection Heading Here}
Subsubsection text here.


% An example of a floating figure using the graphicx package.
% Note that \label must occur AFTER (or within) \caption.
% For figures, \caption should occur after the \includegraphics.
% Note that IEEEtran v1.7 and later has special internal code that
% is designed to preserve the operation of \label within \caption
% even when the captionsoff option is in effect. However, because
% of issues like this, it may be the safest practice to put all your
% \label just after \caption rather than within \caption{}.
%
% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
% option should be used if it is desired that the figures are to be
% displayed while in draft mode.
%
%\begin{figure}[!t]
%\centering
%\includegraphics[width=2.5in]{myfigure}
% where an .eps filename suffix will be assumed under latex, 
% and a .pdf suffix will be assumed for pdflatex; or what has been declared
% via \DeclareGraphicsExtensions.
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure}

% Note that IEEE typically puts floats only at the top, even when this
% results in a large percentage of a column being occupied by floats.


% An example of a double column floating figure using two subfigures.
% (The subfig.sty package must be loaded for this to work.)
% The subfigure \label commands are set within each subfloat command,
% and the \label for the overall figure must come after \caption.
% \hfil is used as a separator to get equal spacing.
% Watch out that the combined width of all the subfigures on a 
% line do not exceed the text width or a line break will occur.
%
%\begin{figure*}[!t]
%\centering
%\subfloat[Case I]{\includegraphics[width=2.5in]{box}%
%\label{fig_first_case}}
%\hfil
%\subfloat[Case II]{\includegraphics[width=2.5in]{box}%
%\label{fig_second_case}}
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure*}
%
% Note that often IEEE papers with subfigures do not employ subfigure
% captions (using the optional argument to \subfloat[]), but instead will
% reference/describe all of them (a), (b), etc., within the main caption.
% Be aware that for subfig.sty to generate the (a), (b), etc., subfigure
% labels, the optional argument to \subfloat must be present. If a
% subcaption is not desired, just leave its contents blank,
% e.g., \subfloat[].


% An example of a floating table. Note that, for IEEE style tables, the
% \caption command should come BEFORE the table and, given that table
% captions serve much like titles, are usually capitalized except for words
% such as a, an, and, as, at, but, by, for, in, nor, of, on, or, the, to
% and up, which are usually not capitalized unless they are the first or
% last word of the caption. Table text will default to \footnotesize as
% IEEE normally uses this smaller font for tables.
% The \label must come after \caption as always.
%
%\begin{table}[!t]
%% increase table row spacing, adjust to taste
%\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of
% \extrarowheight as needed to properly center the text within the cells
%\caption{An Example of a Table}
%\label{table_example}
%\centering
%% Some packages, such as MDW tools, offer better commands for making tables
%% than the plain LaTeX2e tabular which is used here.
%\begin{tabular}{|c||c|}
%\hline
%One & Two\\
%\hline
%Three & Four\\
%\hline
%\end{tabular}
%\end{table}


% Note that the IEEE does not put floats in the very first column
% - or typically anywhere on the first page for that matter. Also,
% in-text middle ("here") positioning is typically not used, but it
% is allowed and encouraged for Computer Society conferences (but
% not Computer Society journals). Most IEEE journals/conferences use
% top floats exclusively. 
% Note that, LaTeX2e, unlike IEEE journals/conferences, places
% footnotes above bottom floats. This can be corrected via the
% \fnbelowfloat command of the stfloats package.




\section{Conclusion}
The conclusion goes here.




% conference papers do not normally have an appendix



% use section* for acknowledgment
\ifCLASSOPTIONcompsoc
  % The Computer Society usually uses the plural form
  \section*{Acknowledgments}
\else
  % regular IEEE prefers the singular form
  \section*{Acknowledgment}
\fi


The authors would like to thank...





% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
\begin{thebibliography}{1}

\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}




% that's all folks
\end{document}



defs.tex
%\newtheorem{theorem}{Theorem}
%\newtheorem{lemma}{Lemma}
%\newtheorem{corollary}{Corollary}

\providecommand{\abs}[1]{\left\lvert#1\right\rvert}
\providecommand{\norm}[1]{\lVert#1\rVert}
\DeclareMathOperator*{\argmax}{argmax}
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\E}{\mathbbm{E}}
\DeclareMathOperator*{\real}{\mathbb{R}}
\DeclareMathOperator*{\onevec}{\mathbbm{1}}
\renewcommand{\algorithmiccomment}[1]{\hfill \eqparbox{COMMENT}{// #1}}

\newcommand{\note}[1]{%
{\color{red} \tt #1}%
}%

package.tex
\usepackage{array}
\usepackage{mdwmath}
\usepackage{mdwtab}
%\usepackage{fixltx2e}
\usepackage{url}
\usepackage{color}
\usepackage[]{graphicx}
\usepackage{epsfig}
\usepackage{bbm}
%\usepackage{setspace}
\usepackage{enumerate}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{cite}
\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{eqparbox}
\usepackage{comment}
%\usepackage{subfigure}
\usepackage[tight,footnotesize]{subfigure}
\usepackage{float}
\usepackage{mathtools}
\usepackage{centernot}
\usepackage{gensymb}
\usepackage{algpseudocode}
\usepackage{caption}
\captionsetup[figure]{skip=5pt}
\captionsetup{font = scriptsize}
\captionsetup[subfigure]{skip=5pt}
%\usepackage{subfig}
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
%\usepackage{multicol}% http://ctan.org/pkg/multicols
\usepackage{comment}

CVPR_2017_arXiv.bbl
\begin{thebibliography}{10}\itemsep=-1pt

\bibitem{hyrumEI13}
H.~S. Anderson, J.~Ilic-Helms, B.~Rohrer, J.~Wheeler, and K.~Larson.
\newblock Sparse imaging for fast electron microscopy, 2013.

\bibitem{atkins1999tree}
C.~B. Atkins, C.~A. Bouman, and J.~P. Allebach.
\newblock Tree-based resolution synthesis.
\newblock In {\em PICS}, pages 405--410, 1999.

\bibitem{boyd2011distributed}
S.~Boyd, N.~Parikh, E.~Chu, B.~Peleato, and J.~Eckstein.
\newblock Distributed optimization and statistical learning via the alternating
  direction method of multipliers.
\newblock {\em Foundations and Trends in Machine Learning}, 3(1):1--122, 2011.

\bibitem{brifman2016turning}
A.~Brifman, Y.~Romano, and M.~Elad.
\newblock Turning a denoiser into a super-resolver using plug and play priors.
\newblock In {\em Image Processing (ICIP), 2016 IEEE International Conference
  on}, pages 1404--1408. IEEE, 2016.

\bibitem{buades2005review}
A.~Buades, B.~Coll, and J.-M. Morel.
\newblock A review of image denoising algorithms, with a new one.
\newblock {\em Multiscale Modeling \& Simulation}, 4(2):490--530, 2005.

\bibitem{chan2014monte}
S.~H. Chan, T.~Zickler, and Y.~M. Lu.
\newblock Monte carlo non-local means: Random sampling for large-scale image
  filtering.
\newblock {\em Image Processing, IEEE Transactions on}, 23(8):3711--3725, 2014.

\bibitem{deheyn2010bioluminescent}
D.~D. Deheyn and N.~G. Wilson.
\newblock Bioluminescent signals spatially amplified by wavelength-specific
  diffusion through the shell of a marine snail.
\newblock {\em Proceedings of the Royal Society of London B: Biological
  Sciences}, page rspb20102203, 2010.

\bibitem{dong2013sparse}
W.~Dong, L.~Zhang, R.~Lukac, and G.~Shi.
\newblock Sparse representation based image interpolation with nonlocal
  autoregressive modeling.
\newblock {\em IEEE Transactions on Image Processing}, 22(4):1382--1394, 2013.

\bibitem{eckstein1992douglas}
J.~Eckstein and D.~P. Bertsekas.
\newblock On the {Douglas-Rachford} splitting method and the proximal point
  algorithm for maximal monotone operators.
\newblock {\em Mathematical Programming}, 55(1-3):293--318, 1992.

\bibitem{eladHarAna05}
M.~Elad, J.-L. Starck, P.~Querre, and D.~Donoho.
\newblock Simultaneous cartoon and texture image inpainting using morphological
  component analysis ({MCA}).
\newblock {\em Applied and Computational Harmonic Analysis}, 19(3):340 -- 358,
  2005.
\newblock Computational Harmonic Analysis - Part 1.

\bibitem{farsiu2004fast}
S.~Farsiu, M.~D. Robinson, M.~Elad, and P.~Milanfar.
\newblock Fast and robust multiframe super resolution.
\newblock {\em Image processing, IEEE Transactions on}, 13(10):1327--1344,
  2004.

\bibitem{freeman2002example}
W.~T. Freeman, T.~R. Jones, and E.~C. Pasztor.
\newblock Example-based super-resolution.
\newblock {\em Computer Graphics and Applications, IEEE}, 22(2):56--65, 2002.

\bibitem{gabay1976dual}
D.~Gabay and B.~Mercier.
\newblock A dual algorithm for the solution of nonlinear variational problems
  via finite element approximation.
\newblock {\em Computers \& Mathematics with Applications}, 2(1):17--40, 1976.

\bibitem{glasner2009super}
D.~Glasner, S.~Bagon, and M.~Irani.
\newblock Super-resolution from a single image.
\newblock In {\em Computer Vision, 2009 IEEE 12th International Conference on},
  pages 349--356. IEEE, 2009.

\bibitem{inpaintReviewSPM14}
C.~Guillemot and O.~Le~Meur.
\newblock Image inpainting : Overview and recent advances.
\newblock {\em Signal Processing Magazine, IEEE}, 31(1):127--144, Jan 2014.

\bibitem{juhl2006assembly}
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