Compressed sensing of block-sparse signals recovery based on subspace

Block-sparse signal is a typical sparse signal. As to the feature of block-sparse signal for compressed sensing, a subspace matching pursuit algorithm for block-sparse signals recovery has been proposed in this paper. The algorithm determines an estimate of the correct support set during each iteration, which includes a subspace of the correct support set, then calculates the residual, additionally, the estimate support set will be refined at next iteration using the backtracking and least mean square criterion. The correct support set will be found until the residual reduces to zero; finally, the recovery signal can be determined by the pseudo-inverse. A sufficient condition for the proposed algorithm is given and proved, which shows it's universally applicable. The algorithm has two important characteristics: high recovery probability because of the backtracking idea; low computational complexity. The simulation results demonstrate its high recovery probability than most existing algorithms, which makes it a promising candidate for block-sparse signals compressed sensing.