Research For Block-Sparse Signal Recovery Algorithm Based On Compress Sensing

In this thesis,we introduce the basic theory about compress sensing and Bayesian compress sensing.Noticed that by introducing the block structure of signals,we can explore the block sparse properties to improve the performance of the signal recovery.We also introduce the block sparse signal algorithm to multiple measurement vectors scenarios.Firstly,we develop a new sparse Bayesian learning method to recover the blocksparse signals.Unlike the traditional sparse Bayesian learning method,the prior of each coefficient not only involves its own hyper-parameters,but also the hyper-parameter of its immediate neighbors.An expectation-maximization(EM)algorithm is proposed to estimate the hyper-parameter of the block-sparse signals.Secondly,we develop our pattern-coupled sparse Bayesian learning method to the multiple measurement vectors(MMV)scenarios.We consider the block-sparse signal recovery problem in the context of MMV signals with common row sparsity pattern.A key assumption in MMV is that the support(i.e.the indexes of non zeros entries)of each column in MMV signals is identical.Existing algorithms consider the common row sparsity patterns of MMV signals using the conventional sparse Bayesian learning framework.The notable difference of our algorithm is that,we develop a patterncoupled hierarchical Gaussian prior method to characterize both the sparseness coefficients and the statistical dependency between neighboring coefficients of the common row sparsity MMV signals.The block structure of the MMV signals is entirely unknown,and the hyper parameters are learned via an expectation-maximization(EM)algorithm.Simulation results shows that our proposed method offer a competitive performance in recovering block-sparse common row sparsity pattern MMV signals.