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Regularization Using a Parameterized Trust Region Subproblem

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ogrodzev2004.pdf (638.38 KB)

Date

2004

Authors

Grodzevich, Oleg

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Publisher

University of Waterloo

Abstract

We present a new method for regularization of ill-conditioned problems that extends the traditional trust-region approach. Ill-conditioned problems arise, for example, in image restoration or mathematical processing of medical data, and involve matrices that are very ill-conditioned. The method makes use of the L-curve and L-curve maximum curvature criterion as a strategy recently proposed to find a good regularization parameter. We describe the method and show its application to an image restoration problem. We also provide a MATLAB code for the algorithm. Finally, a comparison to the CGLS approach is given and analyzed, and future research directions are proposed.

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Keywords

Mathematics, regularization, ill-posed, inverse imaging problem, numerically hard, robustness, algorithms, programming, efficiency, conjugate gradient

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URI

http://hdl.handle.net/10012/1159

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Theses
Combinatorics and Optimization