Truncated Decompositions and Filtering Methods with Reflective/Anti-Reflective Boundary Conditions: A Comparison

• Published in: Matrix Methods: Theory, Algorithms And Applications pp. 382 - 408
• Main Author: Possio, C. Tablino
• Format: Book Chapter
• Language: English
• Published: WORLD SCIENTIFIC 01.04.2010
• Subjects: Matrices and Algorithms; boundary conditions; filtering methods; spectral decompositions
• ISBN: 9812836020; 9789812836014; 9812836012; 9814469556; 9789812836021; 9789814469555
• DOI: 10.1142/9789812836021_0025

The paper analyzes and compares some spectral filtering methods as truncated singular/eigen-value decompositions and Tikhonov/Reblurring regularizations in the case of the recently proposed Reflective [18] and Anti-Reflective [21] boundary conditions. We give numerical evidence to the fact that spectral decompositions (SDs) provide a good image restoration quality and this is true in particular for the Anti-Reflective SD, despite the loss of orthogonality in the associated transform. The related computational cost is comparable with previously known spectral decompositions, and results substantially lower than the singular value decomposition. The model extension to the cross-channel blurring phenomenon of color images is also considered and the related spectral filtering methods are suitably adapted.