Related papers: Uniform multi-penalty regularization for linear il…

The inversion of two-dimensional NMR data is an ill-posed problem related to the numerical computation of the inverse Laplace transform. In this paper we present the 2DUPEN algorithm that extends the Uniform Penalty (UPEN) algorithm…

A crucial issue in two-dimensional Nuclear Magnetic Resonance (NMR) is the speed and accuracy of the data inversion. This paper proposes a multi-penalty method with locally adapted regularization parameters for fast and accurate inversion…

In this paper we study the convex envelopes of a new class of functions. Using this approach, we are able to unify two important classes of regularizers from unbiased non-convex formulations and weighted nuclear norm penalties. This opens…

Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The…

Non-linear differential equations are a fundamental tool to describe different phenomena in nature. However, we still lack a well-established method to tackle stiff differential equations. Here we present a machine learning framework to…

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…

Translating machine learning algorithms into clinical applications requires addressing challenges related to interpretability, such as accounting for the effect of confounding variables (or metadata). Confounding variables affect the…

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…

Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…

In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…

For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…

Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert…

In this paper, we study the Nystr{\"o}m type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nystr{\"o}m type subsampling which is…

This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in…

In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with general convex penalty term. When the data is given exactly, we give a…

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

This paper aims to compare different regularization strategies to address a common phenomenon, severe overfitting, in embedding-based neural networks for NLP. We chose two widely studied neural models and tasks as our testbed. We tried…

In recent studies \cite{ZZ24, FY24}, the Interior Penalty Virtual Element Method (IPVEM) has been developed for solving a fourth-order singular perturbation problem, with uniform convergence established in the lowest-order case concerning…

We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multi-spectral…