Related papers: A class of regularization schemes for linear ill-p…
We consider composite linear inverse problems where the signal to recover is modeled as a sum of two functions. We study a variational framework formulated as an optimization problem over the pairs of components using two regularization…
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…
This paper addresses Tikhonov like regularization methods with convex penalty functionals for solving nonlinear ill-posed operator equations formulated in Banach or, more general, topological spaces. We present an approach for proving…
We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and…
We investigate the Cauchy problem for linear elliptic operators with $C^\infty$-coefficients at a regular set $\Omega \subset R^2$, which is a classical example of an ill-posed problem. The Cauchy data are given at the manifold $\Gamma…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required.…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…
A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization method, differs essentially from the local linearization…
Recently, inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization, many of inverse problems are reduced to linear systems.…
In this paper, two parallel methods for solving systems of accretive operator equations in Banach spaces are studied. The convergence analysis of the methods in both free-noise and noisy data cases is provided.
In this work, we propose a high-order regularization method to solve the ill-conditioned problems in robot localization. Numerical solutions to robot localization problems are often unstable when the problems are ill-conditioned. A typical…
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…
Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…
We study the convergence of variationally regularized solutions to linear ill-posed operator equations in Banach spaces as the noise in the right hand side tends to $0$. The rate of this convergence is determined by abstract smoothness…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
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…
In this article on variational regularization for ill-posed nonlinear problems, we are once again discussing the consequences of an oversmoothing penalty term. This means in our model that the searched-for solution of the considered…
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 present and analyse an approach to image reconstruction problems with imperfect forward models based on partially ordered spaces - Banach lattices. In this approach, errors in the data and in the forward models are described using order…