Regularization Using a Parameterized Trust Region Subproblem

Oleg Grodzevich (ogrodzevuwaterloo.ca)
Henry Wolkowicz (hwolkowiczuwaterloo.ca)

Abstract: We present a new method for regularization of ill-conditioned problems, such as those that arise in image restoration or mathematical processing of medical data. The method extends the traditional {\em trust-region subproblem}, \TRS, approach that makes use of the {\em L-curve} maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We use derivative information, and properties of an algorithm for solving the TRS, to efficiently move along points on the L-curve and reach the point of maximum curvature. We do not find a complete characterization of the L-curve. A MATLAB code for the algorithm is tested and a comparison to the conjugate gradient least squares, CGLS, approach is given and analyzed.

Keywords: regularization, trust region subproblem, ill-conditioned problems, L-curve, image restoration

Category 1: Applications -- Science and Engineering

Category 2: Applications -- Science and Engineering (Biomedical Applications )

Category 3: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation: Research Report CORR 2005-11 University of Waterloo, Waterloo, Canada

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Entry Submitted: 05/18/2005
Entry Accepted: 05/18/2005
Entry Last Modified: 05/18/2005

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