A mismatched greedy pursuit algorithm for sparse spike deconvolution

Matched filter output of pulse compression systems often suffers from sidelobes. In a multi-target environment, these sidelobes can cause false alarms and misdetection. In addition, these sidelobes make it particularly difficult to recover closely located spikes. In this paper, an iterative greedy algorithm is proposed that combines mismatched filtering with matching pursuit algorithm. Recovery bounds for the proposed algorithm are derived and used to show that the proposed algorithm can yield better resolution compared to matching pursuit algorithm.