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Stability of Image-Reconstruction Algorithms

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Publications associées (34)

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Controlled learning of pointwise nonlinearities in neural-network-like architectures

Michaël Unser, Alexis Marie Frederic Goujon, Stanislas Ducotterd

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the second-order tota ...

2025

Towards Trustworthy Deep Learning for Image Reconstruction

Alexis Marie Frederic Goujon

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

EPFL2024

High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

Volkan Cevher, Fanghui Liu

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposi ...

2024

Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks

Rahul Parhi

We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared Euclidean norm of the ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

The inductive bias of deep learning: Connecting weights and functions

Guillermo Ortiz Jimenez

Years of a fierce competition have naturally selected the fittest deep learning algorithms. Yet, although these models work well in practice, we still lack a proper characterization of why they do so. This poses serious questions about the robustness, trus ...

EPFL2023

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

2023

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

Lenka Zdeborová, Florent Gérard Krzakala, 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

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

Understanding Deep Neural Function Approximation in Reinforcement Learning via ϵ-Greedy Exploration

Volkan Cevher, Fanghui Liu, Luca Viano

This paper provides a theoretical study of deep neural function approximation in reinforcement learning (RL) with the ϵ-greedy exploration under the online setting. This problem setting is motivated by the successful deep Q-networks (DQN) framework that fa ...

2022

Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains

Rafael Vazquez Hernandez, Bernard Kapidani

When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mortaring has been shown to be advantageous. This contribu ...

2022

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Fabio Nobile, Sundar Subramaniam Ganesh

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...

2023

Predicting in Uncertain Environments: Methods for Robust Machine Learning

Paul Thierry Yves Rolland

One of the main goal of Artificial Intelligence is to develop models capable of providing valuable predictions in real-world environments. In particular, Machine Learning (ML) seeks to design such models by learning from examples coming from this same envi ...

EPFL2022

High Resolution Interferometric Imaging of Liquid-Solid Interfaces with HOTNNET

John Martin Kolinski, Ramin Kaviani

Background A variety of imaging methods are available to obtain kinematic data at an interface, with a widely varying range of spatial and temporal resolution. These methods require a trade-off between imaging rate and resolution. Objective A deep learning ...

2022

System and method for transcoding spectral data with task-based optimization via symmetric non-negative matrix factorization

Forrest Simon Webler

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

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution

Thomas Jean Debarre

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

EPFL2022

Linear Lipschitz and C-1 extension operators through random projection

Federico Stra

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Learning Lipschitz-Controlled Activation Functions in Neural Networks for Plug-and-Play Image Reconstruction Methods

Michaël Unser, Dimitris Perdios, Alexis Marie Frederic Goujon, Pakshal Narendra Bohra

Ill-posed linear inverse problems are frequently encountered in image reconstruction tasks. Image reconstruction methods that combine the Plug-and-Play (PnP) priors framework with convolutional neural network (CNN) based denoisers have shown impressive per ...

2021

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

A Newton Frank-Wolfe method for constrained self-concordant minimization

Volkan Cevher, Quoc Tran Dinh

We develop a new Newton Frank-Wolfe algorithm to solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO). Unlike L-smooth convex functions, where the Lipschitz continuity of the objective gradient holds gl ...

SPRINGER2022

Contribution of preclinical MRI to responsible animal research: living up to the 3R principle

Ileana Ozana Jelescu

2021