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.

References in corpus (3)

• Robust inversion via semistochastic dimensionality reduction
• Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data
• A variational Bayesian method for inverse problems with impulsive noise

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