Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces

2018/03/29 by Weidling, Frederic, Sprung, Benjamin, Hohage, Thorsten
#65J20 #65J22 #65N21 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1803.11019

Abstract

This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We show order optimal rates of convergence for finitely smoothing operators and for the backwards heat equation for a range of Besov spaces using variational source conditions. We also derive order optimal rates for a white noise model with the help of variational source conditions and concentration inequalities for sharp negative Besov norms of the noise.

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