Alternating Direction Method of Multipliers Based on ℓ_2,0-norm for Multiple Measurement Vector Problem
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In this paper, we propose an alternating direction method of multipliers (ADMM)-based optimization algorithm to achieve better undersampling rate for multiple measurement vector (MMV) problem. The core is to introduce the ℓ_2,0-norm sparsity constraint to describe the joint-sparsity of the MMV problem, which is different from the widely used ℓ_2,1-norm constraint in the existing research. In order to illustrate the better performance of ℓ_2,0-norm, first this paper proves the equivalence of the sparsity of the row support set of a matrix and its ℓ_2,0-norm. Afterward, the MMV problem based on ℓ_2,0-norm is proposed. Moreover, building on the Kurdyka-Lojasiewicz property, this paper establishes that the sequence generated by ADMM globally converges to the optimal point of the MMV problem. Finally, the performance of our algorithm and comparison with other algorithms under different conditions is studied by simulated examples.
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