Stable Outlier-Robust Signal Recovery Over Networks: A Convex Analytic Approach Using Minimax Concave Loss

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

IEEE Transactions on Signal and Information Processing over Networks Pub Date : 2024-08-29 DOI:10.1109/TSIPN.2024.3451992

Maximilian H. V. Tillmann;Masahiro Yukawa

引用次数: 0

Abstract

This paper presents a mathematically rigorous framework of remarkably-robust signal recovery over networks. The proposed framework is based on the minimax concave (MC) loss, which is a weakly convex function so that it attains i) remarkable outlier-robustness and ii) guarantee of convergence to a solution of the posed problem. We present a novel problem formulation which involves an auxiliary vector so that the formulation accommodates statistical properties of signal, noise, and outliers. We show the conditions to guarantee convexity of the local and global objectives. Via reformulation, the distributed triangularly preconditioned primal-dual algorithm is applied to the posed problem. The numerical examples show that our proposed formulation exhibits remarkable robustness under devastating outliers as well as outperforming the existing methods. Comparisons between the local and global convexity conditions are also presented.

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网络上稳定的离群稳健信号恢复：使用最小凹损失的凸分析方法

本文提出了一种在网络上实现显著稳健信号恢复的严谨数学框架。所提出的框架基于最小凹损（MC），它是一个弱凸函数，因此可以实现 i) 显著的离群稳健性和 ii) 保证收敛到所提问题的解决方案。我们提出了一种新颖的问题表述方法，其中涉及一个辅助向量，从而使表述方法能够适应信号、噪声和异常值的统计特性。我们展示了保证局部和全局目标凸性的条件。通过重新表述，分布式三角预条件初等-二元算法被应用于所提出的问题。数值示例表明，我们提出的算法在破坏性异常值条件下表现出显著的鲁棒性，并优于现有方法。此外，还对局部和全局凸性条件进行了比较。

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.