  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.
