Multi-Scale Patch-Based Image Restoration.

Many image restoration algorithms in recent years are based on patch processing. The core idea is to decompose the target image into fully overlapping patches, restore each of them separately, and then merge the results by a plain averaging. This concept has been demonstrated to be highly effective, leading often times to the state-of-the-art results in denoising, inpainting, deblurring, segmentation, and other applications. While the above is indeed effective, this approach has one major flaw: the prior is imposed on intermediate (patch) results, rather than on the final outcome, and this is typically manifested by visual artifacts. The expected patch log likelihood (EPLL) method by Zoran and Weiss was conceived for addressing this very problem. Their algorithm imposes the prior on the patches of the final image, which in turn leads to an iterative restoration of diminishing effect. In this paper, we propose to further extend and improve the EPLL by considering a multi-scale prior. Our algorithm imposes the very same prior on different scale patches extracted from the target image. While all the treated patches are of the same size, their footprint in the destination image varies due to subsampling. Our scheme comes to alleviate another shortcoming existing in patch-based restoration algorithms--the fact that a local (patch-based) prior is serving as a model for a global stochastic phenomenon. We motivate the use of the multi-scale EPLL by restricting ourselves to the simple Gaussian case, comparing the aforementioned algorithms and showing a clear advantage to the proposed method. We then demonstrate our algorithm in the context of image denoising, deblurring, and super-resolution, showing an improvement in performance both visually and quantitatively.