41 Result(s)

Article

Smooth over-parameterized solvers for non-smooth structured optimization

Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp ...

Clarice Poon, Gabriel Peyré in Mathematical Programming (2023)

Article

The Geometry of Off-the-Grid Compressed Sensing

Compressed sensing (CS) ensures the recovery of sparse vectors from a number of randomized measurements proportional to their sparsity. The initial theory considers discretized domains, and the randomness make...

Clarice Poon, Nicolas Keriven, Gabriel Peyré in Foundations of Computational Mathematics (2023)

Article

Ground Metric Learning on Graphs

Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether th...

Matthieu Heitz, Nicolas Bonneel… in Journal of Mathematical Imaging and Vision (2021)

Article

Preface to the Special Issue on Optimization for Data Sciences

Gabriel Peyré, Antonin Chambolle in Applied Mathematics & Optimization (2020)

Article

An Interpolating Distance Between Optimal Transport and Fisher–Rao Metrics

This paper defines a new transport metric over the space of nonnegative measures. This metric interpolates between the quadratic Wasserstein and the Fisher–Rao metrics and generalizes optimal transport to meas...

Lénaïc Chizat, Gabriel Peyré… in Foundations of Computational Mathematics (2018)

Article

JMIV Special Issue Mathematics and Image Analysis

Jalal Fadili, Gitta Kutyniok, Gabriel Peyré… in Journal of Mathematical Imaging and Vision (2017)

Article

Support Recovery for Sparse Super-Resolution of Positive Measures

We study sparse spikes super-resolution over the space of Radon measures on \(\mathbb {R}\) ...

Quentin Denoyelle, Vincent Duval… in Journal of Fourier Analysis and Applicatio… (2017)

Article

The degrees of freedom of partly smooth regularizers

We study regularized regression problems where the regularizer is a proper, lower-semicontinuous, convex and partly smooth function relative to a Riemannian submanifold. This encompasses several popular exampl...

Samuel Vaiter, Charles Deledalle… in Annals of the Institute of Statistical Mat… (2017)

Article

Local Convergence Properties of Douglas–Rachford and Alternating Direction Method of Multipliers

The Douglas–Rachford and alternating direction method of multipliers are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity oper...

**gwei Liang, Jalal Fadili, Gabriel Peyré in Journal of Optimization Theory and Applica… (2017)

Article

Convergence rates with inexact non-expansive operators

In this paper, we present a convergence rate analysis for the inexact Krasnosel’skiĭ–Mann iteration built from non-expansive operators. The presented results include two main parts: we first establish the glob...

**gwei Liang, Jalal Fadili, Gabriel Peyré in Mathematical Programming (2016)

Article

Exact Support Recovery for Sparse Spikes Deconvolution

This paper studies sparse spikes deconvolution over the space of measures. We focus on the recovery properties of the support of the measure (i.e., the location of the Dirac masses) using total variation of me...

Vincent Duval, Gabriel Peyré in Foundations of Computational Mathematics (2015)

Article

Variational Texture Synthesis with Sparsity and Spectrum Constraints

This paper introduces a new approach for texture synthesis. We propose a unified framework that both imposes first order statistical constraints on the use of atoms from an adaptive dictionary, as well as seco...

Guillaume Tartavel, Yann Gousseau… in Journal of Mathematical Imaging and Vision (2015)

Chapter and Conference Paper

Activity Identification and Local Linear Convergence of Douglas–Rachford/ADMM under Partial Smoothness

Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex...

**gwei Liang, Jalal Fadili, Gabriel Peyré… in Scale Space and Variational Methods in Com… (2015)

Chapter

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in imaging sciences, statistics, and machine learning. The goal is to reconstruct an unknown vector from partial indirect, and possibly noisy, meas...

Samuel Vaiter, Gabriel Peyré, Jalal Fadili in Sampling Theory, a Renaissance (2015)

Article

Sliced and Radon Wasserstein Barycenters of Measures

This article details two approaches to compute barycenters of measures using 1-D Wasserstein distances along radial projections of the input measures. The first method makes use of the Radon transform of the m...

Nicolas Bonneel, Julien Rabin, Gabriel Peyré… in Journal of Mathematical Imaging and Vision (2015)