A greedy search algorithm with tree pruning for sparse signal recovery

In this paper, we propose a new sparse recovery algorithm referred to as the matching pursuit with a tree pruning (TMP) that performs efficient combinatoric search with the aid of greedy tree pruning. Two key ingredients of the TMP algorithm are pre-selection to put a restriction on the indices of columns in Φ being investigated and tree pruning to avoid the investigation of unpromising paths in the search. In the noisy setting, we show that TMP identifies the support (index set of nonzero elements) accurately when the signal power is larger than the constant multiple of noise power. In the empirical simulations, we confirm this results by showing that TMP performs close to an ideal estimator (often called Oracle estimate) for high signal-to-noise ratio (SNR) regime.