  Single image superresolution has been a popular research topic in the last
two decades and has recently received a new wave of interest due to deep neural
networks. In this paper, we approach this problem from a different perspective.
With respect to a downsampled low resolution image, we model a high resolution
image as a combination of two components, a deterministic component and a
stochastic component. The deterministic component can be recovered from the
low-frequency signals in the downsampled image. The stochastic component, on
the other hand, contains the signals that have little correlation with the low
resolution image. We adopt two complementary methods for generating these two
components. While generative adversarial networks are used for the stochastic
component, deterministic component reconstruction is formulated as a regression
problem solved using deep neural networks. Since the deterministic component
exhibits clearer local orientations, we design novel loss functions tailored
for such properties for training the deep regression network. These two methods
are first applied to the entire input image to produce two distinct
high-resolution images. Afterwards, these two images are fused together using
another deep neural network that also performs local statistical rectification,
which tries to make the local statistics of the fused image match the same
local statistics of the groundtruth image. Quantitative results and a user
study indicate that the proposed method outperforms existing state-of-the-art
algorithms with a clear margin.
