Publications related to Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization

Anomalous dissipation and other non-smooth phenomena in fluids

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

EPFL2024

Efficient local linearity regularization to overcome catastrophic overfitting

Volkan Cevher, Grigorios Chrysos, Fanghui Liu, Elias Abad Rocamora

Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly w ...

2024

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

Pakshal Narendra Bohra

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

EPFL2024

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Le Chen, David Jean-Michel Candil, Cheuk Yin Lee

We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...

Springer2023

Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

Boris Buffoni

Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The cons ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

A Neural-Network-Based Convex Regularizer for Inverse Problems

Michaël Unser, Stanislas Ducotterd, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in quality. Unfortunately, these new methods often lack reliability and explainability, and there is a growing interest to address these ...

2023

Regularization of polynomial networks for image recognition

Volkan Cevher, Bohan Wang, Grigorios Chrysos

Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method with a promising ...

2023

Regularization of polynomial networks for image recognition

Volkan Cevher, Bohan Wang, Grigorios Chrysos

Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method with a promising ...

Ieee Computer Soc2023

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Michaël Unser

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L\documentclass[12pt]{ ...

Springer2023

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

Graph signal processing tailored for subgraph focus and community structure

Miljan Petrovic

Community structure in graph-modeled data appears in a range of disciplines that comprise network science. Its importance relies on the influence it bears on other properties of graphs such as resilience, or prediction of missing connections. Nevertheless, ...

EPFL2022

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

On the reconstruction of the attenuation function of a return-stroke current from the Fourier Transform of finite-duration measurements

Farhad Rachidi-Haeri, Marcos Rubinstein

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

Combining Model Driven and Data Driven Approaches for Inverse Problems in Parameter Estimation and Image Reconstruction: From Modelling to Validation

Thomas Yu

Machine learning has become the state of the art for the solution of the diverse inverse problems arising from computer vision and medical imaging, e.g. denoising, super-resolution, de-blurring, reconstruction from scanner data, quantitative magnetic reson ...

EPFL2022

Role of stochastic noise and generalization error in the time propagation of neural-network quantum states

Giuseppe Carleo

Neural-network quantum states (NQS) have been shown to be a suitable variational ansatz to simulate out-of-equilibrium dynamics in two-dimensional systems using timedependent variational Monte Carlo (t-VMC). In particular, stable and accurate time propagat ...

SCIPOST FOUNDATION2022

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

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

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

Coarse graining and large-N behavior of the d-dimensional N-clock model

Matthias Ruf, Matthias Benjamin Ruf

We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...

2021

Sparse non-negative super-resolution - simplified and stabilised

Hemant Tyagi, Armin Eftekhari

We consider the problem of non-negative super-resolution, which concerns reconstructing a non-negative signal x = Sigma(k )(i=1)a(i)delta(ti) from m samples of its convolution with a window function phi(s - t), of the form y(s(j)) = Sigma(k)(i=1) a(i) phi( ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Large Steps in Inverse Rendering of Geometry

Wenzel Alban Jakob, Baptiste Alexandre Marie Philippe Claude Nicolet

Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to mi ...

ASSOC COMPUTING MACHINERY2021