Convergence Rates for Inverse Problems with Impulsive Noise
Abstract
We study inverse problems F(f) = g with perturbed right hand side g^{obs} corrupted by so-called impulsive noise, i.e. noise which is concentrated on a small subset of the domain of definition of g. It is well known that Tikhonov-type regularization with an L^1 data fidelity term yields significantly more accurate results than Tikhonov regularization with classical L^2 data fidelity terms for this type of noise. The purpose of this paper is to provide a convergence analysis explaining this remarkable difference in accuracy. Our error estimates significantly improve previous error estimates for Tikhonov regularization with L^1-fidelity term in the case of impulsive noise. We present numerical results which are in good agreement with the predictions of our analysis.
Keywords
Cite
@article{arxiv.1308.2536,
title = {Convergence Rates for Inverse Problems with Impulsive Noise},
author = {Thorsten Hohage and Frank Werner},
journal= {arXiv preprint arXiv:1308.2536},
year = {2015}
}