When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and perturbations. As a result, any method relying on the graph topology may yield suboptimal results if those imperfections are ignored. Motivated by this, we propose a novel approach for handling perturbations on the links of the graph and apply it to the problem of robust graph filter (GF) identification from input-output observations. Different from existing works, we formulate a non-convex optimization problem that operates in the vertex domain and jointly performs GF identification and graph denoising. As a result, on top of learning the desired GF, an estimate of the graph is obtained as a byproduct. To handle the resulting bi-convex problem, we design an algorithm that blends techniques from alternating optimization and majorization minimization, showing its convergence to a stationary point. The second part of the paper i) generalizes the design to a robust setup where several GFs are jointly estimated, and ii) introduces an alternative algorithmic implementation that reduces the computational complexity. Finally, the detrimental influence of the perturbations and the benefits resulting from the robust approach are numerically analyzed over synthetic and real-world datasets, comparing them with other state-of-the-art alternatives.
Least-Squares Adaptive Filter-Based Cohen's Class Time-Frequency Distribution for Signal Denoising
Nanjing University of Information Science and Technology（南京信息工程大学）；Hubei University（湖北大学）；Shanghai Jiao Tong University（上海交通大学）；Nanjing Institute of Technology（南京工程学院）
Optimal Wiener-Filter Solutions for Denoising of Graph Signals on Directed Graphs
Neuro-X Institute, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院神经-X研究所）；Department of Radiology and Medical Informatics, University of Geneva（日内瓦大学放射学与医学信息学系）
Node-Oriented Proactive Spectral Modulation: A Unified Fractional Framework for Graph Signal Denoising
Nanjing University of Information Science and Technology（南京信息工程大学）；Hubei University（湖北大学）；Shanghai Jiao Tong University（上海交通大学）；Nanjing Institute of Technology（南京工程学院）
