Convex Combination of Compressed Sensing Algorithms

In this paper, we propose a new framework for compressed sensing (CS) based on data fusion principles, where several CS algorithms work in parallel to recover a
$K$
-sparse signal, and their outputs are combined convexly using a set of combiner coefficients drawn randomly, followed by a 2K level hard-thresholding, a pursuit step and final pruning by another
$K$
level hard-thresholding. A rigorous convergence analysis is presented and sufficient conditions for convergence are derived. Unlike other existing algorithms which use data fusion concepts but do not employ convex combination of estimates generated by the participating algorithms and instead, use a union of support of individual estimates, the proposed method is free from the restrictions on the number of participating algorithms. Empirically, it is observed that the proposed framework allows us to recover the sparse signal of interest using fewer measurements than required by any individual algorithm. It is further seen that even when some of the participating algorithms do not perform well, the proposed framework is still able to recover the
$K$
-sparse signal maintaining the same level of performance. Simulations also reveal that performance of the proposed framework is either at par or better than that of existing algorithms that apply data fusion.