This dissertation proposed a novel greedy algorithm for the support recovery of a sparse signal from a small number of noisy measurements. In the proposed algorithm, a new support index is identified for each iteration based on bit-wise maximum a posteriori (B-MAP) detection. Bit-Wise MAP detection is optimal in the sense of detecting one of the remaining support indices, provided that all the detected indices in the previous iterations are correct. Despite its optimality, it requires an expensive complexity for computing the maximization metric, (i.e., a posteriori probability of each remaining support) due to the marginalization of high-dimensional sparse vectors. We address this problem by presenting a good proxy, named B-MAP proxy, on the maximization metric which is accurate enough to find the maximum index, rather than an exact probability. Moreover, it is easily evaluated only using vector correlations as in orthogonal matching pursuit (OMP), but using completely different proxy matrices for maximization. We have demonstrated that the proposed B-MAP detection provides a significant gain compared with the existing methods such as OMP and MAP-OMP while maintaining the same complexity. Subsequently, we construct an advanced greedy algorithm based on B-MAP proxy by leveraging the idea of compressive sampling matching pursuit (CoSaMP) and subspace pursuit (SP). Simulation result shows that we show that our B-MAP algorithm outperforms OMP and MAP-OMP under the frameworks of the advanced greedy algorithms.
