论文标题
基于稀疏性多刺光谱估计的数学基础
Mathematical Foundation of Sparsity-based Multi-snapshot Spectral Estimation
论文作者
论文摘要
在本文中，我们研究了估计固定点源位置的频谱估计问题，并在有界域中的傅立叶测量值进行了多个快照。我们旨在为基于稀疏性的超级分辨率在一维空间和多维空间中的这种频谱估计问题中提供数学基础。特别是，我们估计位置恢复的分辨率和稳定性在考虑测量约束下最稀少的解决方案时，并表征了它们对截止频率，噪声水平，点源的稀疏性以及点源振幅向量的不一致。我们的估计值强调了振幅向量在增强多 - 触发光谱估计的分辨率方面的重要性。此外，据我们所知，它还为DOA估计中众所周知的稀疏MMV问题的超分辨率制度提供了第一个稳定性结果。
In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for sparsity-based super-resolution in such spectral estimation problems in both one- and multi-dimensional spaces. In particular, we estimate the resolution and stability of the location recovery when considering the sparsest solution under the measurement constraint, and characterize their dependence on the cut-off frequency, the noise level, the sparsity of point sources, and the incoherence of the amplitude vectors of point sources. Our estimate emphasizes the importance of the high incoherence of amplitude vectors in enhancing the resolution of multi-snapshot spectral estimation. Moreover, to the best of our knowledge, it also provides the first stability result in the super-resolution regime for the well-known sparse MMV problem in DOA estimation.
