A Closed-Form Solution for Graph Signal Separation Based on Smoothness

IF 3 3区计算机科学 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Signal and Information Processing over Networks Pub Date : 2023-11-28 DOI:10.1109/TSIPN.2023.3335615

Mohammad-Hassan Ahmad Yarandi;Massoud Babaie-Zadeh

引用次数: 0

Abstract

Using smoothness criteria to separate smooth graph signals from their summation is an approach that has recently been proposed (Mohammadi et al., 2023) and shown to have a unique solution up to the uncertainty of the average values of source signals. In this correspondence, closed-form solutions of both exact and approximate decompositions of that approach are presented. This closed-form solution in the exact decomposition also answers the open problem of the estimation error. Additionally, in the case of Gaussian source signals in the presence of additive Gaussian noise, it is shown that the optimization problem of that approach is equivalent to the Maximum A Posteriori (MAP) estimation of the sources.

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基于平滑性的图形信号分离闭式解法

使用平滑度标准将平滑图信号从其求和中分离出来是最近提出的一种方法（Mohammadi 等人，2023 年），并证明在源信号平均值的不确定性范围内具有唯一的解决方案。在这篇论文中，介绍了这种方法的精确分解和近似分解的闭式解。精确分解的闭式解也回答了估计误差的开放问题。此外，在存在加性高斯噪声的高斯源信号情况下，该方法的优化问题等同于源的最大后验（MAP）估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Signal and Information Processing over Networks Computer Science-Computer Networks and Communications

CiteScore

5.80

自引率

12.50%

发文量

期刊介绍： The IEEE Transactions on Signal and Information Processing over Networks publishes high-quality papers that extend the classical notions of processing of signals defined over vector spaces (e.g. time and space) to processing of signals and information (data) defined over networks, potentially dynamically varying. In signal processing over networks, the topology of the network may define structural relationships in the data, or may constrain processing of the data. Topics include distributed algorithms for filtering, detection, estimation, adaptation and learning, model selection, data fusion, and diffusion or evolution of information over such networks, and applications of distributed signal processing.