Publications by Julien René Pierre Fageot

PolyCLEAN: Atomic optimization for super-resolution imaging and uncertainty estimation in radio interferometry

Sepand Kashani, Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni, Joan Rue Queralt, Adrian Thibault Etienne Jarret

Context. Imaging in radio interferometry requires solving an ill-posed noisy inverse problem, for which the most adopted algorithm is the original CLEAN algorithm and its variants. Alternative explicit optimization methods have gained increasing attention, ...

EDP SCIENCES S A2025

Convergence analysis of the discretization of continuous-domain inverse problems

Michaël Unser, Julien René Pierre Fageot

We study continuous-domain linear inverse problems that involve a general data-fidelity term and a regularisation term. We consider a regularisation that is formed by the sparsity-promoting total-variation norm, pre-composed with a differential operator th ...

2025

Generalized Bradley-Terry Models for Score Estimation from Paired Comparisons

Le Nguyen Hoang, Julien René Pierre Fageot, Sadegh Farhadkhani, Oscar Jean Olivier Villemaud

Many applications, e.g. in content recommendation, sports, or recruitment, leverage the comparisons of alternatives to score those alternatives. The classical Bradley-Terry model and its variants have been widely used to do so. The historical model conside ...

AAAI Press2024

A Decoupled Approach for Composite Sparse-plus-Smooth Penalized Optimization

Julien René Pierre Fageot, Adrian Thibault Etienne Jarret

We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a different regularizati ...

2024

Complex-order scale-invariant operators and self-similar processes

Michaël Unser, Julien René Pierre Fageot

In this paper, we perform the joint study of scale -invariant operators and self -similar processes of complex order. More precisely, we introduce general families of scale -invariant complex -order fractional -derivation and integration operators by const ...

Academic Press Inc Elsevier Science2024

Comparing various AI approaches to traditional quantitative assessment of the myocardial perfusion in [82Rb] PET for MACE prediction

Adrien Raphaël Depeursinge, Julien René Pierre Fageot, Daniel Abler

Assessing the individual risk of Major Adverse Cardiac Events (MACE) is of major importance as cardiovascular diseases remain the leading cause of death worldwide. Quantitative Myocardial Perfusion Imaging (MPI) parameters such as stress Myocardial Blood F ...

Nature Portfolio2024

TV-based spline reconstruction with Fourier measurements: Uniqueness and convergence of grid-based methods

Julien René Pierre Fageot, Thomas Jean Debarre, Quentin Alain Denoyelle

We study the problem of recovering piecewise-polynomial periodic functions from their low-frequency information. This means that we only have access to possibly corrupted versions of the Fourier samples of the ground truth up to a maximum cutoff frequency ...

ELSEVIER2023

Une version polyatomique de l'algorithme Frank-Wolfe pour résoudre le problème LASSO en grandes dimensions

Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni, Adrian Thibault Etienne Jarret

Nous nous intéressons à la reconstruction parcimonieuse d’images à l’aide du problème d’optimisation régularisé LASSO. Dans de nombreuses applications pratiques, les grandes dimensions des objets à reconstruire limitent, voire empêchent, l’utilisation des ...

2022

Entropic Compressibility of Levy Processes

Julien René Pierre Fageot

In contrast to their seemingly simple and shared structure of independence and stationarity, Levy processes exhibit a wide variety of behaviors, from the self-similar Wiener process to piecewise-constant compound Poisson processes. Inspired by the recent p ...

2022

Steer'n'Detect: fast 2D template detection with accurate orientation estimation

Michaël Unser, Daniel Sage, Zsuzsanna Püspöki, Julien René Pierre Fageot

Motivation: Rotated template matching is an efficient and versatile algorithm to analyze microscopy images, as it automates the detection of stereotypical structures, such as organelles that can appear at any orientation. Its performance however quickly de ...

2022

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Victor Panaretos, Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

2022

The Wavelet Compressibility of Compound Poisson Processes

Julien René Pierre Fageot, Shayan Aziznejad

In this paper, we precisely quantify the wavelet compressibility of compound Poisson processes. To that end, we expand the given random process over the Haar wavelet basis and we analyse its asymptotic approximation properties. By only considering the nonz ...

2022

On the uniqueness of solutions for the basis pursuit in the continuum

Julien René Pierre Fageot, Thomas Jean Debarre

This paper studies the continuous-domain inverse problem of recovering Radon measures on the one-dimensional torus from low-frequency Fourier coefficients, where K (c) is the cutoff frequency. Our approach consists in minimizing the total-variation norm am ...

2022

Principled Design and Implementation of Steerable Detectors

Michaël Unser, Adrien Raphaël Depeursinge, Zsuzsanna Püspöki, Julien René Pierre Fageot

We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown positions and orientations that we aim at retrieving. W ...

2021

Sparsest piecewise-linear regression of one-dimensional data

Michaël Unser, Julien René Pierre Fageot, Thomas Jean Debarre, Quentin Alain Denoyelle

We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there are efficient a ...

Elsevier2021

Dictionary Learning for Two-Dimensional Kendall Shapes

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot, Anna You-Lai Song

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...

SIAM PUBLICATIONS2020

TV-based reconstruction of periodic functions

Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni

We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum ...

IOP PUBLISHING LTD2020

Wavelet analysis of the Besov regularity of Levy white noise

Julien René Pierre Fageot, Shayan Aziznejad

We characterize the local smoothness and the asymptotic growth rate of the Levy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for the local smoothn ...

2020

Gaussian and sparse processes are limits of generalized Poisson processes

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

2020

Support and approximation properties of Hermite splines

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot, Shayan Aziznejad

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

2020