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Some considerations concerning regularization and parameter choice algorithms

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Frank Bauer

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Using a Bayesian-type approach to inverse problems many phenomena occurring in practice can be explained in a consistent way. In particular we can prove a discrete version of the quasi-optimality criterion for choosing the regularization parameter by simply imposing minor additional a priori assumptions about the solution and the measurement noise.


PACS

02.30.Zz Inverse problems

02.60.Pn Numerical optimization

02.70.Hm Spectral methods

02.60.Cb Numerical simulation; solution of equations

05.40.Ca Noise

02.30.Cj Measure and integration

MSC

65J22 Inverse problems

60G40 Stopping times; optimal stopping problems; gambling theory (See also 62L15, 91A60)

49N60 Regularity of solutions

Subjects

Mathematical physics

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 2 (April 2007)

Received 28 June 2006, in final form 29 December 2006

Published 16 March 2007



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