2007/10/28 by Cristina Tablino–Possio, Possio, Cristina Tablino
Engineering · Mathematics · Physics and Astronomy · #65F10 #65F15 #65Y20 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.0710.5272
openalex publication_date 2007/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper analyzes and compares some spectral filtering methods as truncated singular/eigen-value decompositions and Tikhonov/Re-blurring regularizations in the case of the recently proposed Reflective [M.K. Ng, R.H. Chan, and W.C. Tang, A fast algorithm for deblurring models with Neumann boundary conditions, SIAM J. Sci. Comput., 21 (1999), no. 3, pp.851-866] and Anti-Reflective [S. Serra Capizzano, A note on anti-reflective boundary conditions and fast deblurring models, SIAM J. Sci. Comput., 25-3 (2003), pp. 1307-1325] 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.