Compressive subspace fitting for multiple measurement vectors

We study a multiple measurement vector problem (MMV), where multiple signals share a common sparse support and are sampled by a common sensing matrix. While a diversity gain from joint sparsity had been demonstrated earlier in the case of a convex relaxation method using a mixed norm, only recently was it shown that similar gain can be achieved by greedy algorithms if we combine greedy steps with a MUSIC-like subspace criterion. However, the main limitation of these hybrid algorithms is that they require a large number of snapshots or a high signal-to-noise ratio (SNR) for an accurate subspace as well as partial support estimation. Hence, in this work, we show that the noise robustness of these algorithms can be significantly improved by allowing sequential subspace estimation and support filtering, even when the number of snapshots is insufficient. Numerical simulations show that the proposed algorithms significantly outperform the existing greedy algorithms and are quite comparable with computationally expensive state-of-art algorithms.