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Divide and Conquer: Patch-based Image Denoising, Restoration, and Beyond

Presented by: 
Mario Figueiredo Universidade de Lisboa, Instituto Superior Técnico, Lisboa
Thursday 2nd November 2017 - 14:00 to 14:50
INI Seminar Room 1
Patch-based image processing methods can be seen as an application of the “divide and conquer” strategy: since it is admittedly too difficult to formulate a global prior for an entire image, methods in this class process overlapping patches thereof, and combine the results to obtain an image estimate. A particular class of patch-based methods uses Gaussian mixtures models (GMM) to model the patches, in what can be seen as yet another application of the divide and conquer principle, now in the space of patch configurations. Different components of the GMM specialize in modeling different types of typical patch configurations. Although many other statistical image models exist, using a GMM for patches has several relevant advantages: (i) the corresponding minimum mean squared error (MMSE) estimate can be obtained in closed form; (ii) the variance of the estimate can also be computed, providing a principled way to weight the estimates when combining the patch estimates to obtain the full image estimate; (iii) the GMM parameters can be estimated from a dataset of clean patches, from the noisy image itself, or from a combination of the two; (iv) theoretically, a GMM can approximate arbitrarily well any probability density (under mild conditions). In this talk, I will overview the class of patch/GMM-based approaches to image restoration. After reviewing the first members of this family of methods, which simply addressed denoising, I will describe several more recent advances, namely: use of class-adapted GMMs (i.e., tailored to specific image classes, such as faces, fingerprints, text); tackling inverse problems other than denoising (namely, deblurring, hyperspectral super-resolution, compressive imaging), by plugging GMM-based denoisers in the loop of an iterative algorithm (in what has recently been called the plug-and-play approach); joint restoration/segmentation of images; application to blind deblurring. This is joint work with Afonso Teodoro, José Bioucas-Dias, Marina Ljubenović, and Milad Niknejad.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons