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.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/1159 |
| Date | January 2004 |
| Creators | Grodzevich, Oleg |
| Publisher | University of Waterloo |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | application/pdf, 653697 bytes, application/pdf |
| Rights | Copyright: 2004, Grodzevich, Oleg. All rights reserved. |
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