Regularizing linear inverse problems under unknown non-Gaussian white noise allowing repeated measurements. (21st January 2022)

• Record Type: Journal Article
• Authors: Harrach, Bastian; Jahn, Tim; Potthast, Roland
• Is Part Of: IMA journal of numerical analysis. Volume 43:Number 1(2023)
• Page Start: 443
• Page End: 500
• Publication Date: 2022-01-21
• Subjects: statistical inverse problems -- discretization -- white noise -- discrepancy principle; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drab098
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right-hand side is unknown and only accessible through discretized measurements corrupted by white noise with unknown arbitrary distribution. The measuring process can be repeated, which allows to reduce and estimate the measurement error through averaging. We show convergence against the true solution of the infinite-dimensional problem for a priori and a posteriori regularization schemes as the number of measurements and the dimension of the discretization tend to infinity under natural and easily verifiable conditions for the discretization.