B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

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 ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

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 ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

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 ...

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 ...

Situational awareness strategies are essential for the reliable and secure operation of the electric power grid which represents critical infrastructure in modern society. With the rise of converter-interfaced renewable generation and the consequent shift ...

Modern power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). Their presence complicates the analysis and mitigation of harmonics, whose creation and propagation may be amplified ...

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 ...

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

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 ...

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

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 ...

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 ...

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 ...

The usual explanation of the efficacy of wavelet-based methods hinges on the sparsity of many real-world objects in the wavelet domain. Yet, standard wavelet-shrinkage techniques for sparse reconstruction are not competitive in practice, one reason being t ...

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 ...

B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization

Chat with Graph Search

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

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Anomalous dissipation and other non-smooth phenomena in fluids

From low-rank retractions to dynamical low-rank approximation and back

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Efficient local linearity regularization to overcome catastrophic overfitting

Towards Trustworthy Deep Learning for Image Reconstruction

Functional-Basis Analysis of Non-Stationary Signals in Modern Power Grids: Theory and Implementation in Embedded Systems

Unified Harmonic Power-Flow and Stability Analysis of Power Grids with Converter-Interfaced Distributed Energy Resources

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

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

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

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

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

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

A Neural-Network-Based Convex Regularizer for Inverse Problems

The Sparsity of Cycle Spinning for Wavelet-Based Solutions of Linear Inverse Problems

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