Characterizations of variational source conditions, converse results, and maxisets of spectral regularization methods

T Hohage, F Weidling - SIAM Journal on Numerical Analysis, 2017 - SIAM
We describe a general strategy for the verification of variational source condition by
formulating two sufficient criteria describing the smoothness of the solution and the degree …

Data driven regularization by projection

A Aspri, Y Korolev, O Scherzer - Inverse Problems, 2020 - iopscience.iop.org
We study linear inverse problems under the premise that the forward operator is not at hand
but given indirectly through some input-output training pairs. We demonstrate that …

Optimal convergence rates results for linear inverse problems in Hilbert spaces

V Albani, P Elbau, MV de Hoop… - … functional analysis and …, 2016 - Taylor & Francis
In this article, we prove optimal convergence rates results for regularization methods for
solving linear ill-posed operator equations in Hilbert spaces. The results generalizes …

Iteratively regularized Landweber iteration method: convergence analysis via Hölder stability

G Mittal, AK Giri - Applied Mathematics and Computation, 2021 - Elsevier
In this paper, the local convergence of Iteratively regularized Landweber iteration method is
investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly …

On convergence rates of adaptive ensemble Kalman inversion for linear ill-posed problems

F Parzer, O Scherzer - Numerische Mathematik, 2022 - Springer
In this paper we discuss a deterministic form of ensemble Kalman inversion as a
regularization method for linear inverse problems. By interpreting ensemble Kalman …

Lavrentiev's regularization method in Hilbert spaces revisited

B Hofmann, B Kaltenbacher, E Resmerita - arXiv preprint arXiv …, 2015 - arxiv.org
In this paper, we deal with nonlinear ill-posed problems involving monotone operators and
consider Lavrentiev's regularization method. This approach, in contrast to Tikhonov's …

Convergence analysis of inexact Newton–Landweber iteration under Hölder stability

Y Xia, B Han, Z Fu - Inverse Problems, 2022 - iopscience.iop.org
In this paper, we focus on a class of inverse problems with Lipschitz continuous Fréchet
derivatives both in Hilbert spaces and Banach spaces. The convergence and convergence …

Higher order convergence rates for Bregman iterated variational regularization of inverse problems

B Sprung, T Hohage - Numerische Mathematik, 2019 - Springer
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 …

On variational regularization: Finite dimension and Hölder stability

G Mittal, AK Giri - Journal of Inverse and Ill-posed Problems, 2021 - degruyter.com
In this paper, we analyze the convergence rates for finite-dimensional variational
regularization in Banach spaces by taking into account the noisy data and operator …

A unified approach to convergence rates for ℓ1-regularization and lacking sparsity

J Flemming, B Hofmann, I Veselić - Journal of Inverse and Ill-Posed …, 2016 - degruyter.com
In ℓ1-regularization, which is an important tool in signal and image processing, one usually
is concerned with signals and images having a sparse representation in some suitable …