In this paper, we develop a new technique to obtain improved estimates for the computational resolution limits in two-dimensional super-resolution problems and present a new idea for developing two-dimensional super-r...
详细信息
In this paper, we develop a new technique to obtain improved estimates for the computational resolution limits in two-dimensional super-resolution problems and present a new idea for developing two-dimensional super-resolution algorithms. To be more specific, our main contributions are fourfold: (1) Our work improves the resolution estimates for number detection and location recovery in two-dimensional super-resolution problems;(2) 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 sparsitypromoting in solving such problems;(3) Inspired by the 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 (4) 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 some advantages compared to the conventional DOA algorithms.
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