Peter Mathé
WIAS, Berlin, Germany
Statistical learning in inverse problems in Hilbert scales
Abstract:
We study linear ill-posed inverse problems with noisy data in the statistical learning
setting. Approximate reconstructions from random noisy data are sought with general
regularization schemes in Hilbert scales. 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 specific distance functions. For regression functions
with smoothness given in terms of source conditions the error bound can then be
explicitly established.
This is joint work with Abhishake Rastogi, Potsdam.
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