Convergence analysis of (statistical) inverse problems under conditional stability estimates. (19th December 2019)

• Record Type: Journal Article
• Authors: Werner, Frank; Hofmann, Bernd
• Is Part Of: Inverse problems. Volume 36:Number 1(2020)
• Publication Date: 2019-12-19
• Subjects: statistical inverse problems -- conditional stability -- Hilbert scales -- Tikhonov regularization -- Lepskij principle -- convergence rates; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab4cd7
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems in Hilbert scales satisfying conditional stability estimates characterized by general concave index functions. For that case, we exploit Tikhonov regularization and provide convergence and convergence rates of regularized solutions for both deterministic and stochastic noise. We further discuss a priori and a posteriori parameter choice rules and illustrate the validity of our assumptions in different model and real world situations.