Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces
Provides theoretical guarantees for regularization methods in Besov spaces, relevant for inverse problems in imaging and PDEs.
The paper establishes order-optimal convergence rates for Tikhonov regularization with wavelet Besov norm penalties for linear and nonlinear ill-posed problems, including finitely smoothing operators and the backwards heat equation, using variational source conditions.
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.