Inverse learning in Hilbert scales

• URL: http://arxiv.org/abs/2002.10208v1
• Date: Mon, 24 Feb 2020 12:49:54 GMT
• Title: Inverse learning in Hilbert scales
• Authors: Abhishake Rastogi and Peter Math\'e
• Abstract summary: We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of convergence for the regularized solution under the prior assumptions and a certain link condition. We express the error in terms of certain distance functions. For regression functions with smoothness given in terms of source conditions the error bound can then be explicitly established.

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