Signal reconstruction in sensor arrays using sparse representations

We propose a technique of multisensor signal reconstruction based on the assumption, that source signals are spatially sparse, as well as have sparse representation in a chosen dictionary in time domain. This leads to a large scale convex optimization problem, which involves combined l1l1-l2l2 norm minimization. The optimization is carried by the truncated Newton method, using preconditioned conjugate gradients in inner iterations. The byproduct of reconstruction is the estimation of source locations.