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• W3048309030 abstract "We study a non-linear statistical inverse problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization) approach to estimate the quantity for the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonov functional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoretical analysis for the minimizer of the Tikhonov regularization scheme using the concept of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions." @default.
• W3048309030 created "2020-08-13" @default.
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• W3048309030 date "2020-01-01" @default.
• W3048309030 modified "2023-10-18" @default.
• W3048309030 title "Convergence analysis of Tikhonov regularization for non-linear statistical inverse problems" @default.
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• W3048309030 doi "https://doi.org/10.1214/20-ejs1735" @default.
• W3048309030 hasPublicationYear "2020" @default.
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