The Generalized Operator Based Prony Method
The Generalized Operator Based Prony Method
复制标题
DOI：
10.1007/s00365-020-09501-6
复制
发表时间：
2019-01
影响因子：
2.7
通讯作者：
Kilian Stampfer;G. Plonka
中科院分区：
文献类型：
--
作者：
Kilian Stampfer;G. Plonka
广义Prony方法是一种用于多种稀疏信号模型的重建技术，这些模型可以表示为线性算子A的本征函数的稀疏展开。然而，这一过程需要估计线性算子A的更高的幂，这通常是昂贵的。在本文中，我们提出了两个重要的扩展的广义Prony方法，基本上简化了所需的样本的采集，并在同一时间，可以提高数值稳定性的方法。第一个推广是关于算子从A到A的变化，其中A是一个合适的算子值映射，使得A和具有相同的特征函数集。现在的目标是选择这样的幂比A的幂更容易计算。第二个扩展涉及采样泛函的选择。我们展示了如何应用新的不同采样泛函集，其目标是减少算子A（分别）的幂数。在采样方案和简化采集过程的恢复方法。
The generalized Prony method is a reconstruction technique for a large variety of sparse signal models that can be represented as sparse expansions into eigenfunctions of a linear operatorA. However, this procedure requires the evaluation of higher powers of the linear operatorAthat are often expensive to provide. In this paper we propose two important extensions of the generalized Prony method that essentially simplify the acquisition of the needed samples and, at the same time, can improve the numerical stability of the method. The first extension regards the change of operators fromAto, whereis a suitable operator-valued mapping, such thatAandpossess the same set of eigenfunctions. The goal is now to choosesuch that the powers ofare much simpler to evaluate than the powers ofA. The second extension concerns the choice of the sampling functionals. We show how new sets of different sampling functionalscan be applied with the goal being to reduce the needed number of powers of the operatorA(resp.) in the sampling scheme and to simplify the acquisition process for the recovery method.