Regularization Using a Parameterized Trust Region Subproblem

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

Grodzevich, Oleg

University of Waterloo

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

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/1159/1/ogrodzev2004.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 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.