Recovery of signals by a weighted ℓ2/ℓ1 minimization under arbitrary prior support information

Abstract

In this paper, we introduce a weighted ℓ2/ℓ1 minimization method to recover block sparse signals with arbitrary prior support information from a linear model. When partial prior support information is available, a sufficient condition based on the block restricted isometry property is derived to guarantee stable recovery of block sparse signals via weighted ℓ2/ℓ1 minimization. We then show that if the accuracy of every prior block support estimate is at least 50%, the sufficient recovery condition of the weighted ℓ2/ℓ1 minimization is weaker than that of the ℓ2/ℓ1 minimization, and the weighted ℓ2/ℓ1 minimization has better recovery performance than the ℓ2/ℓ1 minimization. Moreover, we illustrate the advantages of the weighted ℓ2/ℓ1 minimization in terms of the recovery performance of block sparse signals under uniform and non-uniform prior information by extensive numerical experiments. The significance of the results lies in the facts that explicitly using block sparsity and partial support information of block sparse signals can achieve better recovery performance than handling the signals as being in the conventional sense, thereby ignoring the additional structure and prior support information in the problem.