Convex Combination of Compressed Sensing Algorithms for Multiple Measurement Vectors

We present a novel data fusion scheme for the multiple measurement vector (MMV) problem arising in compressed sensing. In the proposed MMV-CCCSA framework, a convex combination of the estimates of a
$K$
row-sparse matrix X, produced by a set of different MMV algorithms running in parallel is taken, where the combining coefficients are random and the resulting estimate undergoes a two step process. In the first stage, hard thresholding of level 2K is applied followed by a pursuit step. In the second stage, result of the pursuit step is then hard thresholded by level K, and an another pursuit step is carried out on the resulting estimate completing the process. This estimate is then shared with the participating algorithms, so as to generate the estimate for the next iteration. A rigorous analysis of the proposed MMV-CCCSA is carried out using the restricted isometry property (RIP) of the sensing matrix. We show that under certain mild conditions on the nature of the combining coefficients, the expected value of the distance (in Frobenius sense) between the estimates and the true row-sparse matrix X goes to zero. Extensive simulation studies are also carried out which suggests that the proposed scheme outperforms the existing data fusion models in the literature.