Improved stability conditions of BOGA for noisy block-sparse signals

The block orthogonal greedy algorithm (BOGA) has been proven to successfully recover block-sparse signals in noiseless environments and the associated stability problem dealing with noisy signals has also been studied in the literature. This paper demonstrates that the recovery conditions of the BOGA previously reported can be relaxed by using a different definition of the block-coherence. The presented results in this paper provide a generalization of those reported by Tseng for block-sparse signal and serve as a complement of the BOGA reported by Eldar for noisy signals.

► The stable recovery conditions and the representation error bound of the block orthogonal greedy algorithm (BOGA) for signals with block-sparsity are studied.
► The new theoretical stable recovery conditions are relaxed and the representation error bound is tighter than the previous ones.
► The presented recovery conditions degenerate to those of the orthogonal greedy algorithm for conventional sparse signals.