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We propose a novel greedy algorithm for the support recovery of a sparsesignal from a small number of noisy measurements. In the proposed method, a newsupport index is identified for each iteration based on bit-wise maximum aposteriori (B-MAP) detection. This is optimal in the sense of detecting one ofthe remaining support indices, provided that all the detected indices in theprevious iterations are correct. Despite its optimality, it requires anexpensive complexity for computing the maximization metric (i.e., a posterioriprobability of each remaining support) due to the marginalization ofhigh-dimensional sparse vector. We address this problem by presenting a goodproxy (named B-MAP proxy) on the maximization metric which is accurate enoughto find the maximum index, rather than an exact probability, Moreover, it iseasily evaluated only using vector correlations as in orthogonal matchingpursuit (OMP), but the use completely different proxy matrices formaximization. We demonstrate that the proposed B-MAP detection provides asignificant gain compared with the existing methods as OMP and MAP-OMP, havingthe same complexity. Subsequently, we construct the advanced greedy algorithms,based on B-MAP proxy, by leveraging the idea of compressive sampling matchingpursuit (CoSaMP) and subspace pursuit (SP). Via simulations, we show that theproposed method outperforms also OMP and MAP-OMP under the frameworks of theadvanced greedy algorithms.

Greedy Sparse Signal Recovery Algorithm Based on Bit-wise MAP detection