Super-resolution estimation is the problem of recovering a stream of spikes (point sources) from the noisy observation of a few number 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.

翻译：超级分辨率估计是从对最初几个三角点数的热量观测中恢复一串钉钉(点源)的问题。 超分辨率的性能被确认为与要恢复的钉钉钉之间的分离密切相关。 引入了超分辨率问题的渔业信息矩阵稳定性的新概念, 当FIM的最小电子价值并非在瞬间消失时。 考虑的制度是最小分离与获得的时数成反比的体系。 事实证明, 存在一个分离阈值, 超过此阈值的FIM的机精值可以受不取决于分钟数的数量的约束。 证据取决于FIM的稳定性与Beurling- Selberg箱近距离问题的一般化之间的联系的特征。