相关论文: Graph Denoising with Framelet Regularizer

When approaching graph signal processing tasks, graphs are usually assumed to be perfectly known. However, in many practical applications, the observed (inferred) network is prone to perturbations which, if ignored, will hinder performance.…

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. We decompose an input graph into low-pass and high-pass…

In this paper we show that simple noise regularisation can be an effective way to address GNN oversmoothing. First we argue that regularisers addressing oversmoothing should both penalise node latent similarity and encourage meaningful node…

Image deblurring is relevant in many fields of science and engineering. To solve this problem, many different approaches have been proposed and among the various methods, variational ones are extremely popular. These approaches are…

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…

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…

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…

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…

This paper considers the problem of signal denoising using a sparse tight-frame analysis prior. The L1 norm has been extensively used as a regularizer to promote sparsity; however, it tends to under-estimate non-zero values of the…

Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to…

How to obtain the desirable representation of a 3D shape is a key challenge in 3D shape retrieval task. Most existing 3D shape retrieval methods focus on capturing shape representation with different neural network architectures, while the…

In [DOI:10.1109/ICMEW.2014.6890711], a graph-based denoising is performed by projecting the noisy image to a lower dimensional Krylov subspace of the graph Laplacian, constructed using nonnegative weights determined by distances between…

Inthischapterwediscusshowtolearnanoptimalmanifoldpresentationto regularize nonegative matrix factorization (NMF) for data representation problems. NMF,whichtriestorepresentanonnegativedatamatrixasaproductoftwolowrank nonnegative matrices,…

Networks are widely used in many fields for their powerful ability to provide vivid representations of relationships between variables. However, many of them may be corrupted by experimental noise or inappropriate network inference methods…

Over the last decade, signal processing on graphs has become a very active area of research. Specifically, the number of applications, for instance in statistical or deep learning, using frames built from graphs, such as wavelets on graphs,…

This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…

We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in…

Graph signal processing deals with algorithms and signal representations that leverage graph structures for multivariate data analysis. Often said graph topology is not readily available and may be time-varying, hence (dynamic) graph…

Node classification on graphs is a significant task with a wide range of applications, including social analysis and anomaly detection. Even though graph neural networks (GNNs) have produced promising results on this task, current…

We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…