Sparse recovery from convolved output in underwater acoustic relay networks

This paper explores criteria for unique recovery from blind deconvolution under sparsity priors. Additionally regularizing functions stemming from this problem framework are developed. For key cases, it is possible to ensure unique recoverability given the regularized problem statement. The uniqueness results are informed by a matrix completion-based viewpoint of blind deconvolution. Furthermore, this perspective enables characterization of why blind deconvolution with two sparse inputs is an inherently hard problem. Two blind deconvolution algorithms are proposed which do not rely on alternating between the estimation of one input signal, while holding the other constant. Evaluation of the algorithms is done via simulation and shown to significantly outperform a previously proposed method. Furthermore, numerical illustration of recovery failure considering sparsity of input signals that do not satisfy the recovery constraints is also provided.