Approximate Bit-wise MAP Detection for Greedy Sparse Signal Recovery Algorithms

A greedy algorithm is a fascinating choice in support recovery problem due to its easy implementation and lower complexity compared with other optimization-based algorithms. In this paper, we present a novel greedy algorithm, referred to as bit-wise maximum a posteriori (MAP) detector. In the proposed method, for each iteration, one includes the best index to a target support in the sense of maximizing a posteriori probability given an observation, support indices previously chosen, and a priori information on a sparse vector. In other words, the proposed method employs statistical information on a given sparse recovery system while the other greedy-based algorithms (e.g., orthogonal matching pursuit (OMP)) uses the correlation values in magnitude. We remark that the proposed method has much lower complexity than the (vector-wise) MAP, where the complexity of the former is linear with a sparsity level but the latter is exponential. We further reduce the complexity of the proposed method by efficiently computing a posteriori probability for each iteration. Via simulations, we demonstrate that the proposed method can outperform the other greedy algorithms based on correlations, by exploiting statistical information properly.