Discrepancy Principle for Statistical Inverse Problems with Application to Conjugate Gradient Iteration
Gilles Blanchard and Peter Mathé
Preprint, University of Potsdam Number 2011.07, 2011.

Abstract

The authors discuss the use of the discrepancy principle for statis- tical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well-dened, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modi- cation of the discrepancy is introduced, which takes into account both of the above deciencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration it is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.

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