CIF: Small: Robust Sparse Recovery for Highly Correlated Data

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Most natural signals are inherently sparse in certain bases or dictionaries where they can be approximately represented by only a few significant components carrying the most relevant information. In other words, the intrinsic signal information usually lies in a low-dimensional subspace and the semantic information is often encoded in the sparse representation. Processing of such signals in the sparsified domain is much faster, simpler, and more robust than doing so in the original domain, making sparsity an extremely powerful tool in many classical signal processing applications. Recently, with the emergence of the Compressed Sensing (CS) framework, sparse representation and related optimization problems involving sparsity as a prior called sparse recovery have increasingly attracted the interest of researchers in various diverse disciplines, from statistics, to information theory, applied mathematics, signal processing, coding theory and theoretical computer science.This research involves the analysis, development, and application of robust sparsity-driven algorithms for already-collected highly-correlated data sets where signals often exhibit a high level of joint-sparsity and rich correlation structure. Examples of such data include natural video sequences, volumetric medical images, huge image database, hyperspectral imagery (HSI), and raw synthetic aperture radar (SAR) signals. The research develops a novel unifying robust sparse-recovery framework based on context-aware and observable data-adaptive dictionaries,focusing on two classes of practical applications of sparse recovery: (i) Representative -- denoising, concealment, inpainting, enhancement; and (ii) Discriminative -- clustering, detection, classification, and recognition. Recovery/Discrimination accuracy is greatly improved by taking into account inter-patch spatial correlation, inter-frame temporal correlation, and by adapting algorithms dynamically based on local signal contents as well as by maximizing the level of discrimination within the sparse recovery process.