Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems

Numerical solution of ill-posed problems is often accomplished by discretization (projection onto a finite dimensional subspace) followed by regularization. If the discrete problem has high dimension, though, typically we compute an approximate solution by projecting the discrete problem onto an eve...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 2001-01, Vol.22 (4), p.1204-1221
Main Authors: Kilmer, Misha E., O'Leary, Dianne P.
Format: Article
Language:English
Subjects:
Algorithms
Expected values
Iterative methods
Noise
Regularization methods
Values
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Summary:Numerical solution of ill-posed problems is often accomplished by discretization (projection onto a finite dimensional subspace) followed by regularization. If the discrete problem has high dimension, though, typically we compute an approximate solution by projecting the discrete problem onto an even smaller dimensional space, via iterative methods based on Krylov subspaces. In this work we present a common framework for efficient algorithms that regularize after this second projection rather than before it. We show that determining regularization parameters based on the final projected problem rather than on the original discretization has firmer justification and often involves less computational expense. We prove some results on the approximate equivalence of this approach to other forms of regularization, and we present numerical examples.
ISSN:0895-4798
1095-7162
DOI:10.1137/S0895479899345960