  Multiview super-resolution image reconstruction (SRIR) is often cast as a
resampling problem by merging non-redundant data from multiple low-resolution
(LR) images on a finer high-resolution (HR) grid, while inverting the effect of
the camera point spread function (PSF). One main problem with multiview methods
is that resampling from nonuniform samples (provided by LR images) and the
inversion of the PSF are highly nonlinear and ill-posed problems. Non-linearity
and ill-posedness are typically overcome by linearization and regularization,
often through an iterative optimization process, which essentially trade off
the very same information (i.e. high frequency) that we want to recover. We
propose a novel point of view for multiview SRIR: Unlike existing multiview
methods that reconstruct the entire spectrum of the HR image from the multiple
given LR images, we derive explicit expressions that show how the
high-frequency spectra of the unknown HR image are related to the spectra of
the LR images. Therefore, by taking any of the LR images as the reference to
represent the low-frequency spectra of the HR image, one can reconstruct the
super-resolution image by focusing only on the reconstruction of the
high-frequency spectra. This is very much like single-image methods, which
extrapolate the spectrum of one image, except that we rely on information
provided by all other views, rather than by prior constraints as in
single-image methods (which may not be an accurate source of information). This
is made possible by deriving and applying explicit closed-form expressions that
define how the local high frequency information that we aim to recover for the
reference high resolution image is related to the local low frequency
information in the sequence of views. Results and comparisons with recently
published state-of-the-art methods show the superiority of the proposed
solution.
