Block orthogonal greedy algorithm for stable recovery of block-sparse signal representations

Recently, block-sparse signals, whose nonzero coefficients appearing in blocks, have received much attention. A corresponding block-based orthogonal greedy algorithm (OGA) was proved by Eldar to successfully recover ideal noiseless block-sparse signals under a certain condition on block-coherence. In this paper, the stability problem of block OGA used to recover the noisy block-sparse signals is studied and the corresponding approximation bounds are derived. The theoretical bounds presented in this paper are more general and are proven to include those reported by Donoho and Tseng. Numerical experimental results are presented to support the validity and correctness of theoretical derivation. The simulation results also show that in the noisy case, the block OGA can be proved to achieve better reconstruction performance than the OGA when the conventional sparse signals are represented in block-sparse forms.