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Compressive Sensing (CS), as a newly developed branch of sparse signal processing and representation approaches, has quickly found various applications in a large number of research topics in modern digital signal processing area. This work is devoted to investigating some effective CS and sparse signal processing schemes and approaches, and also to adapting the sparse signal processing idea and CS framework to some specific applications such as object-based surveillance video compression. In compressive sensing, the sampling strategy and reconstruction algorithms are two major components. In this thesis, we first investigate the optimization of the sampling matrix for effective CS performance. An optimizing method, by using a simple polynomial shrink function and a detector to estimate the convergence to stop the iterations early, is proposed to provide better CS performance. A number of experimental simulations are presented to demonstrate the optimized measurement matrix’s effectiveness. Then, a novel Backtracking-based Adaptive Orthogonal Matching Pursuit (BAOMP) method is proposed to effectively reconstruct or approximate the sparse solutions for CS and other sparse representation problems. Different from other Orthogonal Matching Pursuit (OMP)-type algorithms, the proposed method incorporates a backtracking step to more carefully choose the reliable support set, and at the same time, it does not require the signal’s sparsity level to be known before reconstruction. Various experiments on exact sparse signal reconstruction case, noisy signal or noisy measurement approximation case, and two-dimensional (2-D)

Improvements to sparse signal processing in compressive sensing and other methods