Greedy sparse signal reconstruction from sign measurements

This paper presents Matched Sign Pursuit (MSP), a new greedy algorithm to perform sparse signal reconstruction from signs of signal measurements, i.e., measurements quantized to 1-bit. The algorithm combines the principle of consistent reconstruction with greedy sparse reconstruction. The resulting MSP algorithm has several advantages, both theoretical and practical, over previous approaches. Although the problem is not convex, the experimental performance of the algorithm is significantly better compared to reconstructing the signal by treating the quantized measurement as values. Our results demonstrate that combining the principle of consistency with a sparsity prior outperforms approaches that use only consistency or only sparsity priors.