Sparse support recovery from multiple measurement vectors (MMV) is studied in this letter. For years, a noticeable mismatch exists between the theories and algorithms in the research of super-resolution and direction-of-arrival (DOA) estimation that variants of separation conditions are assumed to ensure stable recovery while the corresponding algorithms rarely exploit such structural constraints. Due to the discrete nature of the separation condition, we propose to incorporate such prior information in a Mixed Integer Programming (MIP) problem with an $\ell _{0}$-based constraint. We develop a specialized branch and bound (B&B) algorithm that can efficiently exploit the separation prior with guaranteed complexity reduction. Moreover, we show that computational complexity can be further reduced by leveraging the sparse array idea along with a particular perspective formulation of the MIP. The superior performance of the proposed algorithm is demonstrated via numerical experiments.

中文翻译：

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具有分离先验的关联感知联合支持恢复

在这封信中研究了从多个测量向量 (MMV) 中的稀疏支持恢复。多年来，在超分辨率和到达方向 (DOA) 估计的研究中，理论和算法之间存在明显的不匹配，即假设分离条件的变体以确保稳定的恢复，而相应的算法很少利用这种结构约束。由于分离条件的离散性，我们建议将这些先验信息合并到混合整数规划（MIP）问题中$\ell _{0}$-基于约束。我们开发了一种专门的分支定界 (B&B) 算法，可以有效地利用分离先验并保证降低复杂性。此外，我们表明，通过利用稀疏数组的想法以及 MIP 的特定透视公式，可以进一步降低计算复杂度。通过数值实验证明了所提出算法的优越性能。