A weighted $\ell_1$-minimization for distributed compressive sensing

Distributed Compressive Sensing (DCS) studies the recovery of jointly sparse signals. Compared to separate recovery, the joint recovery algorithms in DCS are usually more effective as they make use of the joint sparsity. In this thesis, we study a weighted l1-minimization algorithm for the joint sparsity model JSM-1 proposed by Baron et al. Our analysis gives a sufficient null space property for the joint sparse recovery. Furthermore, this property can be extended to stable and robust settings. We also presents some numerical experiments for this algorithm.