Greedy subspace pursuit for joint sparse recovery

Abstract

In the joint sparse recovery, where the objective is to recover a signal matrix X-0 of size n x l or a set Omega of its nonzero row indices from incomplete measurements, subspace-based greedy algorithms improving MUSIC such as subspace-augmented MUSIC and sequential compressive MUSIC have been proposed to improve the reconstruction performance of X-0 and Omega with a computational efficiency even when rank(X-0) <= k := vertical bar Omega vertical bar. However, the main limitation of the MUSIC-like methods is that they most likely fail to recover the signal when a partial support estimate of k - rank(X-0) indices for their input is not fully correct. We proposed a computationally efficient algorithm called two-stage iterative method to detect the remained support (T-IDRS), its special version termed by two-stage orthogonal subspace matching pursuit (TSMP), and its variant called TSMP with sparse Bayesian learning (TSML) by exploiting more than the sparsity k to estimate the signal matrix. They improve on the MUSIC-like methods such that these are guaranteed to recover the signal and its support while the existing MUSIC-like methods will fail in the practically significant case of MMV when rank(X-0)/k is sufficiently small. Numerical simulations demonstrate that the proposed schemes have low complexities and most likely outperform other related methods. A condition of the minimum m required for TSMP to recover the signal matrix is derived in the noiseless case to be applicable to a wide class of the sensing matrix. (C) 2018 Elsevier B.V. All rights reserved.