Regularization Using a Parameterized Trust Region Subproblem

[摘要] 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.

[发布机构] University of Waterloo

[效力级别] regularization

[关键词] Mathematics;regularization;ill-posed;inverse imaging problem;numerically hard;robustness;algorithms;programming;efficiency;conjugate gradient