Related papers: Bayesian Formulations for Graph Spectral Denoising

In supervised learning for image denoising, usually the paired clean images and noisy images are collected or synthesised to train a denoising model. L2 norm loss or other distance functions are used as the objective function for training.…

Raman spectroscopy can provide insight into the molecular composition of cells and tissue. Consequently, it can be used as a powerful diagnostic tool, e.g. to help identify changes in molecular contents with the onset of disease. But robust…

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…

In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the…

Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying principle is that neural networks trained on large datasets have…

Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…

Explicit noise-level conditioning is widely regarded as essential for the effective operation of Graph Diffusion Models (GDMs). In this work, we challenge this assumption by investigating whether denoisers can implicitly infer noise levels…

Recovering an image from a noisy observation is a key problem in signal processing. Recently, it has been shown that data-driven approaches employing convolutional neural networks can outperform classical model-based techniques, because…

We investigate the dynamical sampling space-time trade-off problem within a graph setting. Specifically, we derive necessary and sufficient conditions for space-time sampling that enable the reconstruction of an initial band-limited signal…

We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end,…

What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on…

Prior probability models are a fundamental component of many image processing problems, but density estimation is notoriously difficult for high-dimensional signals such as photographic images. Deep neural networks have provided…

In modern contexts, some types of data are observed in high-resolution, essentially continuously in time. Such data units are best described as taking values in a space of functions. Subject units carrying the observations may have…

It is very common to face classification problems where the number of available labeled samples is small compared to their dimension. These conditions are likely to cause underdetermined settings, with high risk of overfitting. To improve…

Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is…

Removal or cancellation of noise has wide-spread applications for imaging and acoustics. In every-day-life applications, denoising may even include generative aspects, which are unfaithful to the ground truth. For scientific use, however,…

In this work we propose a random graph model that can produce graphs at different levels of sparsity. We analyze how sparsity affects the graph spectra, and thus the performance of graph neural networks (GNNs) in node classification on…

Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. A single GNN layer typically consists of a feature transformation and a feature aggregation operation. The former normally uses…

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…

We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…