论文标题
几乎最佳的分辨率估计值，用于二维超级分辨率和一种新算法，用于到达估算方向，均匀矩形阵列
Nearly optimal resolution estimate for the two-dimensional super-resolution and a new algorithm for direction of arrival estimation with uniform rectangular array
论文作者
论文摘要
在本文中，我们开发了一种新技术，以获得APPL中引入的计算分辨率限制的几乎最佳估计。计算。哈蒙。肛门。 56（2022）402-446; IEEE Trans。 inf。理论67（7）（2021）4812-4827;逆probl。 37（10）（2021）104001对于二维超分辨率问题。我们的主要贡献是五倍：（i）我们的工作改善了二维超级分辨率问题的数量检测和位置恢复的分辨率估计值，几乎是最佳的； （ii）因此，我们在二维超级分辨率问题（或到达问题的方向（DOA））中得出了促进稀疏性算法的稳定性结果。稳定性结果在解决此类问题时表现出稀疏性的最佳性能。 （iii）我们的技术为改善高维超级分辨率的分辨率限制的估计铺平了道路，以至于几乎最佳的估计值； （iv）受这些新技术的启发，我们提出了一种基于二维DOA估计的新的基于坐标的模型订单检测算法，理论上证明了其最佳性能，（v）我们还提出了一种新的基于坐标的音乐算法，用于二维DOA估计中的超级分辨源。与传统的DOA算法相比，它具有出色的性能，并具有许多优势。坐标组合的想法似乎是多维DOA估计的一种有希望的方法。
In this paper, we develop a new technique to obtain nearly optimal estimates of the computational resolution limits introduced in Appl. Comput. Harmon. Anal. 56 (2022) 402-446; IEEE Trans. Inf. Theory 67(7) (2021) 4812-4827; Inverse Probl. 37(10) (2021) 104001 for two-dimensional super-resolution problems. Our main contributions are fivefold: (i) Our work improves the resolution estimate for number detection and location recovery in two-dimensional super-resolution problems to nearly optimal; (ii) As a consequence, we derive a stability result for a sparsity-promoting algorithm in two-dimensional super-resolution problems (or Direction of Arrival problems (DOA)). The stability result exhibits the optimal performance of sparsity promoting in solving such problems; (iii) Our techniques pave the way for improving the estimate for resolution limits in higher-dimensional super-resolutions to nearly optimal; (iv) Inspired by these new techniques, we propose a new coordinate-combination-based model order detection algorithm for two-dimensional DOA estimation and theoretically demonstrate its optimal performance, and (v) we also propose a new coordinate-combination-based MUSIC algorithm for super-resolving sources in two-dimensional DOA estimation. It has excellent performance and enjoys many advantages compared to the conventional DOA algorithms. The coordinate-combination idea seems to be a promising way for multi-dimensional DOA estimation.
