Performance guarantees of signal recovery via block-OMP with thresholding

Block-sparsity is an extension of the ordinary sparsity in the realm of the sparse signal representation. Exploiting the block structure of the sparsity pattern, recovery may be possible under more general conditions. In this study, a block version of the orthogonal matching pursuit with thresholding (block-OMPT) algorithm is proposed. Compared with the block version of the orthogonal matching pursuit (block-OMP), block-OMPT works in a less greedy fashion in order to improve the efficiency of the support estimation in iterations. Using the block restrict isometry property (block-RIP), some performance guarantees of block-OMPT are discussed for the bounded noise case and Gaussian noise case. A relationship between block-RIP and block-coherence is obtained. Numerical experiments are provided to illustrate the validity of the authors' main results.