Publication

Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems

Publications associées (37)

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.

Connectez-vous pour utiliser Chat avec Graph Search

Bayes-optimal Learning of Deep Random Networks of Extensive-width

Florent Gérard Krzakala, Lenka Zdeborová, Hugo Chao Cui

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width ...

2023

(S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stability

Nicolas Henri Bernard Flammarion, Scott William Pesme, Mathieu Even

In this paper, we investigate the impact of stochasticity and large stepsizes on the implicit regularisation of gradient descent (GD) and stochastic gradient descent (SGD) over diagonal linear networks. We prove the convergence of GD and SGD with macroscop ...

2023

In this paper we fully describe the trajectory of gradient flow over diagonal linear networks in the limit of vanishing initialisation. We show that the limiting flow successively jumps from a saddle of the training loss to another until reaching the minim ...

2023

A computer-implemented method for reconstructing/recovering high-resolution visible light spectral data at a target resolution d, that comprises obtaining a configuration of a low- resolution multi-channel imaging sensor of resolution p, the configuration ...

2022

A correct representation of the lightning current is crucial when the electromagnetic field radiated to a point of interest has to be computed. Based on the engineering models of Transmission Line type, such representation involves the knowledge of the ret ...

2022

Comparison of non-parametric T2 relaxometry methods for myelin water quantification

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

Multi-component T2 relaxometry allows probing tissue microstructure by assessing compartment-specific T2 relaxation times and water fractions, including the myelin water fraction. Non-negative least squares (NNLS) with zero-order Tikhonov regularization is ...

2021

Geodesic Distance on Optimally Regularized Functional Connectomes Uncovers Individual Fingerprints

Enrico Amico

Background: Functional connectomes (FCs) have been shown to provide a reproducible individual fingerprint, which has opened the possibility of personalized medicine for neuro/psychiatric disorders. Thus, developing accurate ways to compare FCs is essential ...

MARY ANN LIEBERT, INC2021

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

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

, ,

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