Abstract
A prominent property of natural images is that groups of
similar patches within them tend to lie on low-dimensional
subspaces. This property has been previously used for
image denoising, with particularly notable success via
weighted nuclear norm minimization (WNNM). In this paper, we extend the WNNM method into a general image restoration algorithm, capable of handling arbitrary degradations (e.g. blur, missing pixels, etc.). Our approach is based
on a novel regularization term which simultaneously penalizes for high weighted nuclear norm values of all the patch
groups in the image. Our regularizer is isolated from the
data-term, thus enabling convenient treatment of arbitrary
degradations. Furthermore, it exploits the fractal property
of natural images, by accounting for patch similarities also
across different scales of the image. We propose a variable
splitting method for solving the resulting optimization problem. This leads to an algorithm that is quite different from
“plug-and-play” techniques, which solve image-restoration
problems using a sequence of denoising steps. As we verify through extensive experiments, our algorithm achieves
state of the art results in deblurring and inpainting, outperforming even the recent deep net based methods