论文标题
M $^2 $ - 谱估计：一种灵活的方法，以确保理性解决方案
M$^2$-Spectral Estimation: A Flexible Approach Ensuring Rational Solutions
论文作者
论文摘要
本文涉及在多维域上定义的多元（即矢量值）信号的光谱估计问题，该信号缩写为M $^2 $。该问题的提出是为了解决非负术语度量的有限数量的三角矩方程，该方程在系统和控制文献中被称为\ emph {协方差扩展问题}。 This inverse problem and its various generalizations have been extensively studied in the past three decades, and they find applications in diverse fields such as modeling and system identification, signal and image processing, robust control, circuit theory, etc. In this paper, we address the challenging M$^2$ version of the problem, and elaborate on a solution technique via convex optimization with the $τ$-divergence family.作为这项工作的主要贡献，我们表明，通过正确选择发散索引的参数，最佳频谱是一个有理函数，即，解决方案是一个光谱密度，可以根据许多实际应用所需的有限维系统来表示。
This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite number of trigonometric moment equations for a nonnegative matricial measure, which is well known as the \emph{covariance extension problem} in the literature of systems and control. This inverse problem and its various generalizations have been extensively studied in the past three decades, and they find applications in diverse fields such as modeling and system identification, signal and image processing, robust control, circuit theory, etc. In this paper, we address the challenging M$^2$ version of the problem, and elaborate on a solution technique via convex optimization with the $τ$-divergence family. As a major contribution of this work, we show that by properly choosing the parameter of the divergence index, the optimal spectrum is a rational function, that is, the solution is a spectral density which can be represented by a finite-dimensional system, as desired in many practical applications.
