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Block sparse signal recovery from sparsely corrupted measurements

In this study two algorithms are compared in order to reconstruct a block sparse signal from sparsely corrupted measurements using Compressive Sampling / Compressed Sensing (CS). Compressive sampling / Compressed sensing (CS) is a new area of signal processing and attracts too much attention in recent years. Compressive sampling states that if a signal having length N has a sparse representation on an orthonormal basis, then it is possible to recover this signal exactly from M≪N measurements. Two algorithms are studied to reconstruct the original signal one is based on optimization and the other is based on greedy algorithms.