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 $\ell_{2,0}$-norm sparsity constraint to describe the joint-sparsity of the MMV problem, which is different from the widely used $\ell_{2,1}$-norm constraint in the existing research. In order to illustrate the better performance of $\ell_{2,0}$-norm, first this paper proves the equivalence of the sparsity of the row support set of a matrix and its $\ell_{2,0}$-norm. Afterward, the MMV problem based on $\ell_{2,0}$-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.

翻译：本文提出了一种基于交替方向乘子法（ADMM）的优化算法，用于提升多测量向量（MMV）问题中的欠采样率。核心在于引入$\ell_{2,0}$范数稀疏约束来描述MMV问题的联合稀疏性，这与现有研究中广泛使用的$\ell_{2,1}$范数约束不同。为阐明$\ell_{2,0}$范数的优越性能，本文首先证明了矩阵行支撑集的稀疏性与其$\ell_{2,0}$范数的等价性，进而提出了基于$\ell_{2,0}$范数的MMV问题。此外，基于Kurdyka-Lojasiewicz性质，本文证明了ADMM生成的序列全局收敛于MMV问题的最优点。最后，通过仿真算例研究了所提算法在不同条件下的性能，并与其他算法进行了对比分析。