English

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Convergence rates for inverse problems with impulsive noise.

MPS-Authors
/persons/resource/persons129903

Werner,  F.
Research Group of Statistical Inverse-Problems in Biophysics, MPI for Biophysical Chemistry, Max Planck Society;

Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

Hohage, T., & Werner, F. (2014). Convergence rates for inverse problems with impulsive noise. SIAM Journal on Numerical Analysis, 52(3), 1203-1221. doi:10.1137/130932661.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0019-7ECD-2
Abstract
We study inverse problems $F(f) =g$ with perturbed right-hand side $g^{\rm obs}$ 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 $\mathbf{L}^1$ data fidelity term yields significantly more accurate results than Tikhonov regularization with classical $\mathbf{L}^2$ 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 $\mathbf{L}^1$-fidelity term in the case of impulsive noise. We present numerical results which are in good agreement with the predictions of our analysis.