论文标题
关于超分辨率的稳定性和贝尔林 - 塞尔伯格型极端问题
On the Stability of Super-Resolution and a Beurling-Selberg Type Extremal Problem
论文作者
论文摘要
超分辨率估计是从对其第一个三角学矩的嘈杂观察中恢复尖峰（点源）的问题。超分辨率的性能被认为与恢复尖峰之间的分离密切相关。当FIM的最小特征值并非渐近消失时，引入了超分辨率问题的Fisher信息矩阵（FIM）的稳定概念。考虑到最小分离的制度与获得的力矩数量成反比。结果表明，存在一个分离阈值，在该阈值之上，FIM的特征值可以由不取决于矩数的数量来界定。证明依赖于表征FIM稳定性与Beurling-Selberg盒近似问题的概括之间的连接。
Super-resolution estimation is the problem of recovering a stream of spikes (point sources) from the noisy observation of a few numbers of its first trigonometric moments. The performance of super-resolution is recognized to be intimately related to the separation between the spikes to recover. A novel notion of stability of the Fisher information matrix (FIM) of the super-resolution problem is introduced when the minimal eigenvalue of the FIM is not asymptotically vanishing. The regime where the minimal separation is inversely proportional to the number of acquired moments is considered. It is shown that there is a separation threshold above which the eigenvalues of the FIM can be bounded by a quantity that does not depend on the number of moments. The proof relies on characterizing the connection between the stability of the FIM and a generalization of the Beurling-Selberg box approximation problem.
