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How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…

In this paper, we provide a Graph Fourier Transform based approach to downsample signals on graphs. For bandlimited signals on a graph, a test is provided to identify whether signal reconstruction is possible from the given downsampled…

There exist many scenarios where pixel information is available only on a non-regular subset of pixel positions. For further processing, however, it is required to reconstruct such images on a regular grid. Besides many other algorithms,…

Choosing an appropriate frequency definition and norm is critical in graph signal sampling and reconstruction. Most previous works define frequencies based on the spectral properties of the graph and use the same frequency definition and…

State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…

Graph sampling theory extends the traditional sampling theory to graphs with topological structures. As a key part of the graph sampling theory, subset selection chooses nodes on graphs as samples to reconstruct the original signal. Due to…

Various methods to deal with graph data have been proposed in recent years. However, most of these methods focus on graph feature aggregation rather than graph pooling. Besides, the existing top-k selection graph pooling methods have a few…

Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…

In this paper, we define a concept of signal matched multirate whitening filter bank which provides an optimum coding gain. This is achieved by whitening the outputs, of the analysis filter bank, within as well as across the channels, by…

Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions: selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques…

Nonstationary Gabor frames, recently introduced in adaptive signal analysis, represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. Due to the lack of a…

We consider the problem of sampling k-bandlimited graph signals, ie, linear combinations of the first k graph Fourier modes. We know that a set of k nodes embedding all k-bandlimited signals always exists, thereby enabling their perfect…

The increasing availability of geometric data has motivated the need for information processing over non-Euclidean domains modeled as manifolds. The building block for information processing architectures with desirable theoretical…

Deep convolutional neural networks (CNNs) are usually over-parameterized, which cannot be easily deployed on edge devices such as mobile phones and smart cameras. Existing works used to decrease the number or size of requested convolution…

The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…

Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…

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…

Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…

We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…