Related papers: Conjugate phase retrieval on graphs and with appli…
In this note we show that stable recovery of complex-valued signals $x\in\mathbb{C}^n$ up to global sign can be achieved from the magnitudes of $4n-1$ Fourier measurements when a certain "symmetrization and zero-padding" is performed before…
Sampling and interpolation have been extensively studied, in order to reconstruct or estimate the entire graph signal from the signal values on a subset of vertexes, of which most achievements are about continuous signals. While in a lot of…
We prove a sampling theorem for infinite-dimensional Paley-Wiener spaces on graphs which allows for stable frame reconstruction. We prove that all sampling sets for a fixed Paley-Wiener space are complements of lambda-sets (i.e. sets where…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…
In computer vision tasks, features often come from diverse representations, domains (e.g., indoor and outdoor), and modalities (e.g., text, images, and videos). Effectively fusing these features is essential for robust performance,…
Let $\Gamma$ be a connected bridgeless metric graph, and fix a point $v$ of $\Gamma$. We define combinatorial iterated integrals on $\Gamma$ along closed paths at $v$, a unipotent generalization of the usual cycle pairing and the…
Network processes are often represented as signals defined on the vertices of a graph. To untangle the latent structure of such signals, one can view them as outputs of linear graph filters modeling underlying network dynamics. This paper…
Large-scale graph machine learning is challenging as the complexity of learning models scales with the graph size. Subsampling the graph is a viable alternative, but sampling on graphs is nontrivial as graphs are non-Euclidean. Existing…
Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that…
While many multiple graph inference methodologies operate under the implicit assumption that an explicit vertex correspondence is known across the vertex sets of the graphs, in practice these correspondences may only be partially or…
A notion of Paley-Wiener spaces is introduced on combinatorial graphs. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such…
While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum,…
We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $.…
The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a…
Graph signal processing has become an essential tool for analyzing data structured on irregular domains. While conventional graph shift operators (GSOs) are effective for certain tasks, they inherently lack flexibility in modeling…
We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume…
A large number of real-world networks include multiple types of nodes and edges. Graph Neural Network (GNN) emerged as a deep learning framework to generate node and graph embeddings for downstream machine learning tasks. However, popular…
The classical phase retrieval problem involves estimating a signal from its Fourier magnitudes (power spectrum) by leveraging prior information about the desired signal. This paper extends the problem to compact groups, addressing the…