Greedy Sparse Signal Recovery with Tree Pruning

Abstract: Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the support (index set of nonzero elements) of the sparse signals. Well-known drawback of the greedy approach is that the chosen candidate is often not the optimal solution due to the myopic decision in each iteration. In this paper, we propose a greedy sparse recovery algorithm investigating multiple promising candidates via the tree search. Two key ingredients of the proposed algorithm, referred to as the matching pursuit with a tree pruning (TMP), to achieve efficiency in the tree search are the {\it pre-selection} to put a restriction on columns of the sensing matrix to be investigated and the {\it tree pruning} to eliminate unpromising paths from the search tree. In our performance guarantee analysis and empirical simulations, we show that TMP is effective in recovering sparse signals in both noiseless and noisy scenarios.