Asymptotic behaviour of the minimum bound method for choosing the regularization parameter

Lukas, M.A. (1998) Asymptotic behaviour of the minimum bound method for choosing the regularization parameter. Inverse Problems, 14 (1). pp. 149-159.

Abstract

We consider a parameter choice method (called the minimum bound method) for regularization of linear ill-posed problems that was developed by Raus and Gfrerer for the case with continuous, deterministic data. The method is adapted and analysed in a discrete, stochastic framework. It is shown that asymptotically, as the number of data points approaches infinity, the method (with a constant set to 2) behaves like an unbiased error method, which selects the parameter by minimizing a certain unbiased estimate of the expected squared error in the regularized solution. The method is also shown to be weakly asymptotically optimal, in that the 'expected' estimate achieves the optimal rate of convergence with repect to the expected squared error criterion and it has the optimal rate of decay.

Item Type:	Journal Article
Murdoch Affiliation(s):	School of Mathematical and Physical Sciences
Publisher:	Institute of Physics
Copyright:	© 1998 IOP Publishing Ltd
URI:	http://researchrepository.murdoch.edu.au/id/eprint/15200

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