Related papers: Regularisation, optimisation, subregularity
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
Learning methods in Banach spaces are often formulated as regularization problems which minimize the sum of a data fidelity term in a Banach norm and a regularization term in another Banach norm. Due to the infinite dimensional nature of…
We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
We consider Tikhonov-type variational regularization of ill-posed linear operator equations in Banach spaces with general convex penalty functionals. Upper bounds for certain error measures expressing the distance between exact and…
Tikhonov regularization involves minimizing the combination of a data discrepancy term and a regularizing term, and is the standard approach for solving inverse problems. The use of non-convex regularizers, such as those defined by trained…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized…
The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on…
In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The approach is based on the idea of variational inequalities,…
We consider ill-posed linear operator equations with operators acting between Banach spaces. For solution approximation, the methods of choice here are projection methods onto finite dimensional subspaces, thus extending existing results…
In this article we investigate an inexact iterative regularization method based on generalized Bregman distances of an optimal control problem with control constraints. We show robustness and convergence of the inexact Bregman method under…
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…
In this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced directly in the Newton iterate with regularization parameter proportional to the square…
This work addresses the problem of error concealment in video transmission systems over noisy channels employing Bregman divergences along with regularization. Error concealment intends to improve the effects of disturbances at the…
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…
We consider the nonstationary iterated Tikhonov regularization in Banach spaces which defines the iterates via minimization problems with uniformly convex penalty term. The penalty term is allowed to be non-smooth to include $L^1$ and total…
Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…
We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…