相关论文: Risk hull method and regularization by projections…

The generic risk estimator addresses the problem of denoising images corrupted by additive white noise without placing any restriction on the statistical distribution of the noise. In this paper, we discuss an efficient FPGA implementation…

In this work, we propose a new criterion for choosing the regularization parameter in Tikhonov regularization when the noise is white Gaussian. The criterion minimizes a lower bound of the predictive risk, when both data norm and noise…

Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this…

We are concerned with structured $\ell_0$-norms regularization problems, with a twice continuously differentiable loss function and a box constraint. This class of problems have a wide range of applications in statistics, machine learning…

In this paper we present a method for the regularized solution of nonlinear inverse problems, based on Ivanov regularization (also called method of quasi solutions or constrained least squares regularization). This leads to the minimization…

This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a…

In this paper, we investigate regularization of linear inverse problems with irregular noise. In particular, we consider the case that the noise can be preprocessed by certain adjoint embedding operators. By introducing the consequent…

In this work, we address the solution of both linear and nonlinear ill-posed inverse problems by developing a novel graph-based regularization framework, where the regularization term is formulated through an iteratively updated graph…

We address the problem of image denoising in additive white noise without placing restrictive assumptions on its statistical distribution. In the recent literature, specific noise distributions have been considered and correspondingly,…

Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov's discrepancy…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

This paper is concerned with the regularization of large-scale discrete inverse problems by means of inexact Krylov methods. Specifically, we derive two new inexact Krylov methods that can be efficiently applied to unregularized or…

We study the stability of regularization by projection for solving linear inverse problems if the forward operator is given indirectly but specified via some input-output training pairs. We extend the approach in "Data driven regularization…

In this paper, we establish robustness to noise perturbations of polyhedral regularization of linear inverse problems. We provide a sufficient condition that ensures that the polyhedral face associated to the true vector is equal to that of…

Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles, we develop a projectional approach to inverse problems that addresses the…

The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to…

Stein's unbiased risk estimate (SURE) was proposed by Stein for the independent, identically distributed (iid) Gaussian model in order to derive estimates that dominate least-squares (LS). In recent years, the SURE criterion has been…

This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…

We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to $p$-norms, $p \geq 1$. We propose a black-box reduction method that, by employing properties…