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Convergence rates for inverse problems with impulsive noise.

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.

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Genre: Journal Article

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Creators:
Hohage, T., Author
Werner, F.1, Author
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1Research Group of Statistical Inverse-Problems in Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_1113580

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Free keywords: impulsive noise, Banach space regularization, inverse problems, signal processing
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.

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Language(s): eng - English
Dates: 2014-05-15
Publication Status: Published online
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Rev. Method: Peer
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Title: SIAM Journal on Numerical Analysis
Source Genre: Journal
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Pages: - Volume / Issue: 52 (3) Sequence Number: - Start / End Page: 1203 - 1221 Identifier: -