Improving Noise Robustness in Subspace-Based Joint Sparse Recovery

Abstract

In a multiple measurement vector problem (MMV), where multiple signals share a common sparse support and are sampled by a common sensing matrix, we can expect joint sparsity to enable a further reduction in the number of required measurements. While a diversity gain from joint sparsity had been demonstrated earlier in the case of a convex relaxation method using an l 1 /l 2 mixed norm penalty, only recently was it shown that similar diversity 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 often require a large number of snapshots or a high signal-to-noise ratio (SNR) for an accurate subspace as well as partial support estimation. One of the main contributions of this work is to 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 a novel sequential compressive MUSIC (sequential CS-MUSIC) that combines the sequential subspace estimation and support filtering steps significantly outperforms the existing greedy algorithms and is quite comparable with computationally expensive state-of-art algorithms.

A practical subspace multiple measurement vectors algorithm for cooperative spectrum sensing

“…In the literature, subspace-based algorithms [16], [17] have been applied to MMVs. Especially, [16] improves [17] to maintain detection quality with less measurement vectors when noise interference exists.…”

“…In the literature, subspace-based algorithms [16], [17] have been applied to MMVs. Especially, [16] improves [17] to maintain detection quality with less measurement vectors when noise interference exists. In this paper, we modify [16] to adapt to our stopping criteria without needing to use the prior knowledge regarding sparsity.…”

“…Especially, [16] improves [17] to maintain detection quality with less measurement vectors when noise interference exists. In this paper, we modify [16] to adapt to our stopping criteria without needing to use the prior knowledge regarding sparsity. The derived stopping criteria are able to overcome the problem of unknown sparsity, and it can maintain good support detection rate.…”

“…The existing MMVs greedy algorithms rely on some prior knowledge in that [9], [14], [16] have to know sparsity K and [14] and [16] need the relationship between K and L: [14] and [16] require L ≥ K and L < K, respectively. Here, we introduce a practical subspace MMVs greedy (PS-MMVs-G) algorithm without depending on the above prior knowledge.…”

“…For the purpose of precise recovery, augmented subspace is proposed in [16] to extend from Y to merge both column subset of A and Y as a new basis, which is also the subspace of Range(A(Θ)) in noiseless cases, to enhance support detection. The detail will be described in Sec.…”