Related papers: Two-Channel Critically-Sampled Graph Filter Banks …

This paper presents a class of multi-channel cosine-modulated filter banks satisfying the perfect reconstruction (PR) property using an IIR prototype filter. By imposing a suitable structure on the polyphase filter coefficients, we show…

Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data,…

We propose interpretable graph neural networks for sampling and recovery of graph signals, respectively. To take informative measurements, we propose a new graph neural sampling module, which aims to select those vertices that maximally…

Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…

We consider a random geometric graph with vertices sampled from a probability measure supported on $\mathbb R^d$, and study its connectivity. We show the graph is typically disconnected, unless the sampling density has superexponential…

Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to…

Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…

To increase the flexibility and scalability of deep neural networks for image reconstruction, a framework is proposed based on bandpass filtering. For many applications, sensing measurements are performed indirectly. For example, in…

Graph neural networks (GNNs) have been used effectively in different applications involving the processing of signals on irregular structures modeled by graphs. Relying on the use of shift-invariant graph filters, GNNs extend the operation…

Spectral graph neural networks (GNNs) learn graph representations via spectral-domain graph convolutions. However, most existing spectral graph filters are scalar-to-scalar functions, i.e., mapping a single eigenvalue to a single filtered…

Many materials have distinct spectral profiles. This facilitates estimation of the material composition of a scene at each pixel by first acquiring its hyperspectral image, and subsequently filtering it using a bank of spectral profiles.…

This paper expands on the previously described reflectionless filters - that is, filters having, in principle, identically-zero reflection coefficient at all frequencies - by introducing a wide variety of new reflectionless structures that…

A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…

This paper builds theoretical foundations for the recovery of a newly proposed class of smooth graph signals, approximately bandlimited graph signals, under three sampling strategies: uniform sampling, experimentally designed sampling and…

Choosing a uniformly sampled simple directed graph realization of a degree sequence has many applications, in particular in social networks where self-loops are commonly not allowed. It has been shown in the past that one can perform a…

This paper investigates the recovery of a node-domain sparse graph signal from the output of a graph filter. This problem, which is often referred to as the identification of the source of a diffused sparse graph signal, is seminal in the…

Separating multiple graph signals from a single observed mixture is an inherently ill-posed problem that traditionally relies on restrictive and handcrafted priors. This letter addresses this challenge by proposing an unsupervised learnable…

Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph…

Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in…

Considering the problem of nonlinear and non-gaussian filtering of the graph signal, in this paper, a robust square root unscented Kalman filter based on graph signal processing is proposed. The algorithm uses a graph topology to generate…