论文标题
修改Prony的方法，用于恢复和稀疏近似值的通用指数总和
Modifications of Prony's Method for the Recovery and Sparse Approximation of Generalized Exponential Sums
论文作者
论文摘要
在本调查中，我们描述了Prony方法的一些修改。特别是，我们考虑将一般扩展恢复到一阶线性差分运算符的本征函数中，并显示如何使用广义移动运算符从功能样本中恢复这些扩展。我们为广义恢复方法得出了一种类似于ESPRIT的算法，并表明该方法可直接用于从非平衡数据中重建经典的指数总和。此外，我们通过指数和导致非线性最小二乘问题的指数总和来得出Prony的稀疏近似方法的修改。
In this survey we describe some modifications of Prony's method. In particular, we consider the recovery of general expansions into eigenfunctions of linear differential operators of first order and show, how these expansions can be recovered from function samples using generalized shift operators. We derive an ESPRIT-like algorithm for the generalized recovery method and show, that this approach can be directly used to reconstruct classical exponential sums from non-equispaced data. Furthermore, we derive a modification of Prony's method for sparse approximation with exponential sums which leads to a non-linear least-squares problem.
