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It has been shown that iterative reweighted strategies will often improve the performance of many sparse reconstruction algorithms. Iterative Framework for Sparse Reconstruction Algorithms (IFSRA) is a recently proposed method which iteratively enhances the performance of any given arbitrary sparse reconstruction algorithm. However, IFSRA assumes that the sparsity level is known. Forward-Backward Pursuit (FBP) algorithm is an iterative approach where each iteration consists of consecutive forward and backward stages. Based on the IFSRA, this paper proposes the Iterative Forward-Backward Pursuit (IFBP) algorithm, which applies the iterative reweighted strategies to FBP without the need for the sparsity level. By using an approximate iteration strategy, IFBP gradually iterates to approach the unknown signal. Finally, this paper demonstrates that IFBP significantly improves the reconstruction capability of the FBP algorithm, via simulations including recovery of random sparse signals with different nonzero coefficient distributions in addition to the recovery of a sparse image. [ABSTRACT FROM AUTHOR]

In this paper, an iterative Compressive Sensing (CS) algorithm is proposed for acoustical source characterization problems with block sparsity constraints. Source localization and signal separation are accomplished in a unified CS framework. The inverse problem is formulated with the Equivalent Source Method as a linear underdetermined system of equations. As conventional approaches based on convex optimization can be computationally expensive and fail to deal with continuously distributed sources, the proposed approach that is adapted from the Newton's method and is augmented with a special pruning procedure is capable of solving the inverse problem far more efficiently with comparable accuracy. The pruning procedure employs a binary mask that admits sparsity constraints of two-dimensional block sources. The binary mask is heuristic in that it tends to promote nonzero positive source magnitudes. In each iteration, the source amplitude vector is on one hand updated by the Newton's method and on the other hand pruned with the binary mask. With the pruning procedure, the source magnitudes become increasingly sparse and clustered such that the block characteristics are enhanced. In the post-processing phase, particle velocity is calculated on the basis of the equivalent source amplitudes. Numerical and experimental investigations are conducted to validate the proposed technique. The results have demonstrated the efficacy of the proposed Compressive Newton's method in imaging block sources and extracting signal waveforms with little computational cost, as compared to a convex optimization package. [ABSTRACT FROM AUTHOR]

Missing data is a commonly encountered and challenging issue in data-driven process analysis. Several methods that attempt to estimate missing observations for the purpose of control, identification, etc. have been developed over the decades. However, existing methods tend to produce erroneous estimates when the percentage of missing data is high and mostly do not exploit the benefit of parsimonious or sparse signal representations. Recently developed compressed sensing (CS) techniques are naturally suited to handle the problem of missing data recovery since they provide powerful signal recovery methods that take advantage of sparse representations of signals in a set of functions, known as the overcomplete dictionary . A majority of these signal recovery algorithms assume that the dictionary is known beforehand. This paper presents a method to estimate missing observations using CS ideas, but with an adaptive learning of the overcomplete dictionary from data. The method is particularly devised for signals that have a block-diagonal sparse representation, an assumption that is not too restrictive. An iterative optimization method, consisting of an iterative CS problem on block-segmented data, for discovering this sparsifying dictionary is presented. Further, we present theoretical and practical guidelines for the segmentation size. It is shown that the error at each iteration is bounded for the exact, i.e., zero model mismatch and noise-free, case. Demonstrations on five different systems illustrate the efficacy of the proposed method with respect to recovery of missing data and convergence properties. Finally, the method is observed to require fewer observations than a fixed dictionary for a given reconstruction accuracy. [ABSTRACT FROM AUTHOR]