Regularization Using a Parameterized Trust Region Subproblem
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Date
2004
Authors
Grodzevich, Oleg
Journal Title
Journal ISSN
Volume Title
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