论文标题
基于多群集结构的超级分辨点源的基于测量解耦合的快速算法
A measurement decoupling based fast algorithm for super-resolving point sources with multi-cluster structure
论文作者
论文摘要
我们考虑了从界面域中从其傅立叶数据中解决一个维点源的问题的问题。古典子空间方法（例如音乐算法，矩阵铅笔方法等）在解决紧密间隔的来源方面表现出极大的优势，但是它们的计算成本通常很重。对于具有多群集结构的点源，尤其是这种情况，它需要处理大型数据矩阵，这是由高度采样的测量结果产生的。为了解决这个问题，我们根据测量解耦策略提出了一种称为D Music的快速算法。从理论上讲，对于具有已知群集结构的点源，可以通过求解通过使用多极基础获得的线性方程系统来将它们的测量源分解为每个集群的局部测量。我们进一步开发了一种亚采样算法来检测群集结构并利用它将全局测量分离。最后，将音乐算法应用于每个本地测量，以解决其中的点源。与标准音乐算法相比，所提出的算法具有可比的超分辨能力，同时具有较低的计算复杂性。
We consider the problem of resolving closely spaced point sources in one dimension from their Fourier data in a bounded domain. Classical subspace methods (e.g., MUSIC algorithm, Matrix Pencil method, etc.) show great superiority in resolving closely spaced sources, but their computational cost is usually heavy. This is especially the case for point sources with a multi-cluster structure which requires processing large-sized data matrix resulted from highly sampled measurements. To address this issue, we propose a fast algorithm termed D-MUSIC, based on a measurement decoupling strategy. We demonstrate theoretically that for point sources with a known cluster structure, their measurement can be decoupled into local measurements of each of the clusters by solving a system of linear equations that are obtained by using a multipole basis. We further develop a subsampled MUSIC algorithm to detect the cluster structure and utilize it to decouple the global measurement. In the end, the MUSIC algorithm was applied to each local measurement to resolve point sources therein. Compared to the standard MUSIC algorithm, the proposed algorithm has comparable super-resolving capability while having a much lower computational complexity.
