Expectation maximisation‐based approach to recovering multiple sparse signals with common sparsity pattern

The problem of simultaneously recovering multiple sparse signals bearing a common sparsity pattern is addressed. Specifically, a common Gaussian prior to all the sparse signals under consideration is assigned. This can make that the signals share the same sparsity pattern. Then, an expectation maximisation (EM)‐based approach to learn the priori parameters from measurements, thereby leading to the recovery of sparse signals is adopted. Simulations verify that the proposed EM approach outperforms the state‐of‐the‐art counterparts.