Related papers: Bayesian Formulations for Graph Spectral Denoising

A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important…

Geometric data analysis relies on graphs that are either given as input or inferred from data. These graphs are often treated as "correct" when solving downstream tasks such as graph signal denoising. But real-world graphs are known to…

We study the graph signal denoising problem by estimating a piecewise constant signal over an undirected graph. We propose a new Bayesian approach that first converts a general graph to a chain graph via the depth-first search algorithm,…

This paper presents a novel Bayesian strategy for the estimation of smooth signals corrupted by Gaussian noise. The method assumes a smooth evolution of a succession of continuous signals that can have a numerical or an analytical…

Modelling noisy data in a network context remains an unavoidable obstacle; fortunately, random matrix theory may comprehensively describe network environments effectively. Thus it necessitates the probabilistic characterisation of these…

In recent years, graph signal processing (GSP) technology has become popular in various fields, and graph Laplacian regularizers have also been introduced into convolutional sparse representation. This paper proposes a convolutional sparse…

We propose a denoising method for multimodal graph signals by an alternating minimization scheme that sequentially solves signal restoration and graph learning problems. Many complex-structured data, i.e., those on sensor networks, can…

Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the…

We study the problem of sampling and reconstructing spectrally sparse graph signals where the objective is to select a subset of nodes of prespecified cardinality that ensures interpolation of the original signal with the lowest possible…

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the…

In spectroscopic experiments, data acquisition in multi-dimensional phase space may require long acquisition time, owing to the large phase space volume to be covered. In such case, the limited time available for data acquisition can be a…

Semi-supervised learning on real-world graphs is frequently challenged by heterophily, where the observed graph is unreliable or label-disassortative. Many existing graph neural networks either rely on a fixed adjacency structure or attempt…

In this paper, we propose a Bayesian MAP estimator for solving the deconvolution problems when the observations are corrupted by Poisson noise. Towards this goal, a proper data fidelity term (log-likelihood) is introduced to reflect the…

In this paper, we propose an interpretable denoising method for graph signals using regularization by denoising (RED). RED is a technique developed for image restoration that uses an efficient (and sometimes black-box) denoiser in the…

On one hand, the transmitted ultrasound beam gets attenuated as propagates through the tissue. On the other hand, the received Radio-Frequency (RF) data contains an additive Gaussian noise which is brought about by the acquisition card and…

There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…

We propose an interpretable graph neural network framework to denoise single or multiple noisy graph signals. The proposed graph unrolling networks expand algorithm unrolling to the graph domain and provide an interpretation of the…

Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…

In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…

Despite remarkable success in diverse web-based applications, Graph Neural Networks(GNNs) inherit and further exacerbate historical discrimination and social stereotypes, which critically hinder their deployments in high-stake domains such…