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Related publications (27)

Fourier interpolation on the real line

Maryna Viazovska

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,+/- 1,+/- ...

2019

Graph-Based Detection of Seams In 360-Degree Images

Pascal Frossard, Francesca De Simone, Sohyeong Kim, Roberto Gerson De Albuquerque Azevedo

In this paper, we propose an algorithm to detect a specific kind of distortions, referred to as seams, which commonly occur when a 360-degree image is represented in planar domain by projecting the sphere to a polyhedron, e.g, via the Cube Map (CM) project ...

2019

Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We study one-dimensional continuous-domain inverse problems with multiple generalized total-variation regularization, which involves the joint use of several regularization operators. Our starting point is a new representer theorem that states that such in ...

2019

Exact Diffusion for Distributed Optimization and Learning-Part I: Algorithm Development

Ali H. Sayed, Bicheng Ying, Kun Yuan

This paper develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II of this paper to have a wider stability range an ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta, Thomas Jean Debarre

We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our met ...

IEEE2019

Slepian Guided Filtering of Graph Signals

Dimitri Nestor Alice Van De Ville, Miljan Petrovic

Joint localization of graph signals in vertex and spectral domain is achieved in Slepian vectors calculated by either maximizing energy concentration (mu) or minimizing modified embedded distance (xi) in the subgraph of interest. On the other hand, graph L ...

SPIE-INT SOC OPTICAL ENGINEERING2019

Fourier could be a data scientist: From graph Fourier transform to signal processing on graphs

Pierre Vandergheynst, Benjamin Ricaud, Nicolas Tremblay

The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that the Fourier transform is. The flexibility of this analysis, its computational efficiency and the physical interpretation it offers makes it a cornerstone in many ...

ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER2019

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