Publication

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Publications associées (50)

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Michaël Unser

Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...
2020

Matrix recovery from bilinear and quadratic measurements

Martin Vetterli, Adam James Scholefield, Michalina Wanda Pacholska, Karen Adam

Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a linear one, but it ...
ArXiv2020

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

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 ...
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

Sparse Dictionaries for Continuous-Domain Inverse Problems

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We study 1D continuous-domain inverse problems for multicomponent signals. The prior assumption on these signals is that each component is sparse in a different dictionary specified by a regularization operators. We introduce a hybrid regularization functi ...
2019

Robust myelin water imaging from multi-echo T2 data using second-order Tikhonov regularization with control points

Jean-Philippe Thiran, Tobias Kober, Tom Hilbert, Erick Jorge Canales Rodriguez, Marco Pizzolato, Gian Franco Piredda, Alessandro Daducci, Nicolas Kunz

Myelin water imaging is an MRI technique used to quantify myelination in the brain. The state-of-the-art reconstruction method is based on non-negative least squares optimization with zero-order Tikhonov regularization. In this study, a second-order Tikhon ...
2019

Efficient Greedy Coordinate Descent for Composite Problems

Martin Jaggi, Sebastian Urban Stich, Anastasiia Koloskova, Sai Praneeth Reddy Karimireddy

Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension ...
2019

Efficient Greedy Coordinate Descent for Composite Problems

Martin Jaggi, Sebastian Urban Stich, Anastasiia Koloskova, Sai Praneeth Reddy Karimireddy

Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension ...
MICROTOME PUBLISHING2019

Inverse Analysis of Radiative Flux Maps for the Characterization of High Flux Sources

Sophia Haussener, Clemens Gregor Suter, Gaël Jean Clément Levêque

The reconstruction of the angular and spatial intensity distribution from radiative flux maps measured in high flux solar simulators or optical concentrators is an ill-posed inverse problem requiring special solution strategies. We aimed at providing a sol ...
2019

Graph Chatbot

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.