Iterative Reweighted Algorithms for Sparse Signal Recovery with Temporally Correlated Source Vectors

Iterative reweighted algorithms, as a class of algorithms for sparse signal recovery, have been found to have better performance than their non-reweighted counterparts. However, for solving the problem of multiple measurement vectors (MMVs), all the existing reweighted algorithms do not account for temporal correlation among source vectors and thus their performance degrades significantly in the presence of correlation. In this work we propose an iterative reweighted sparse Bayesian learning (SBL) algorithm exploiting the temporal correlation, and motivated by it, we propose a strategy to improve existing reweighted $\ell_2$ algorithms for the MMV problem, i.e. replacing their row norms with Mahalanobis distance measure. Simulations show that the proposed reweighted SBL algorithm has superior performance, and the proposed improvement strategy is effective for existing reweighted $\ell_2$ algorithms.Comment: Accepted by ICASSP 201

Joint Sparsity with Different Measurement Matrices

We consider a generalization of the multiple measurement vector (MMV) problem, where the measurement matrices are allowed to differ across measurements. This problem arises naturally when multiple measurements are taken over time, e.g., and the measurement modality (matrix) is time-varying. We derive probabilistic recovery guarantees showing that---under certain (mild) conditions on the measurement matrices---l2/l1-norm minimization and a variant of orthogonal matching pursuit fail with a probability that decays exponentially in the number of measurements. This allows us to conclude that, perhaps surprisingly, recovery performance does not suffer from the individual measurements being taken through different measurement matrices. What is more, recovery performance typically benefits (significantly) from diversity in the measurement matrices; we specify conditions under which such improvements are obtained. These results continue to hold when the measurements are subject to (bounded) noise.Comment: Allerton 201