Research On Block Sparse Signal Reconstruction Algorithms

As an important topic in compressive sensing,sparse reconstruction can recover high-dimensional signals with low-dimensional measurements.Traditional sparse representation techniques assume that the nonzero elements in the sparse signal are randomly located.However,for most real sparse signals,the non-zero elements often have block structure.Exploiting the structures of sparse signals can create a more accurate model and hence improve the reconstruction performace.Therefore,the research on block sparse signal reconstruction algorithms has important research significance and practical values.In this paper,we investigate the block sparse signal reconstruction.The theory of block sparse signal and block sparse reconstruction algorithms are studied first.Then,we conduct research on the recovery methods of block sparse signal with unknown block structures.By studying the pattern coupled sparse Bayesian learning(PCSBL)algorithm,we find that the PCSBL method considers the sparsity patterns of the neighboring coefficients to be related to each other and uses a predefined parameter to control the relevance between the hyperparameters.However,for most real signals with block sparsity,the degree of relevance between neighboring coefficients is inhomogeneous,and should be data-dependent.This motivates us to modify PCSBL by replacing the single predefined parameter with a set of data-dependent coupling parameters to capture the relevance.In this paper,by performing a linear transformation to the independent hyperparameters,a set of correlated hyperparameters is generated to build the hierarchical Gaussian prior model for recovery of block sparse signals.The coupling parameters which compose the transformation matrix are estimated by the expectation maximization(EM)principle.The relevance between the hyperparameters is data dependent so the sparsity patterns of neighboring coefficients are related in an adaptive way.Compared with existing block sparse recovery methods,our approach is able to encourage the block sparse structure in a more flexible and more reliable way.In order to reduce the risk of overfitting,we have simplified the hierarchical model of the new algorithm by assigning one coupling parameter to each hyperparameter.The simplified algorithm can not only reduce the computation complexity of the algorithm,but also avoid the problem of overfitting to some extent.