On-grid based direction-of-arrival (DOA) estimation methods rely on the resolution of a difficult group-sparse optimization problem that involves the $\ell _{2,0}$ pseudo-norm. In this work, we show that an exact relaxation of this problem can be obtained by replacing the $\ell _{2,0}$ term with a group minimax concave penalty with suitable parameters. This relaxation is more amenable to non-convex optimization algorithms as it is continuous and admits less local (not global) minimizers than the initial $\ell _{2,0}$-regularized criteria. We then show on numerical simulations that the minimization of the proposed relaxation with an iteratively reweighted $\ell _{2,1}$ algorithm leads to an improved performance over traditional approaches.

中文翻译：

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通过精确连续 l$_\text{2,0}$-Norm Relaxation 估计到达方向

基于网格的到达方向 (DOA) 估计方法依赖于一个困难的群稀疏优化问题的解决，该问题涉及 $\ell _{2,0}$伪规范。在这项工作中，我们表明可以通过替换$\ell _{2,0}$具有合适参数的组极小极大凹惩罚项。这种松弛更适合非凸优化算法，因为它是连续的，并且比初始的局部（非全局）极小值更少$\ell _{2,0}$- 规范化的标准。然后我们在数值模拟中展示了通过迭代重新加权来最小化建议的松弛$\ell _{2,1}$ 算法比传统方法提高了性能。