Anti-reflective (AR) boundary conditions (BC) have been introduced recently in connection with fast deblurring algorithms, both in the case of signals and images. Here we extend such BCs to d dimensions (d ≥ 1) and we study in detail the algebra induced by the AR-BCs, with strongly symmetric point spread functions (PSF), both from a structural and computational point of view. The use of the re-blurring idea and the computational features of the AR-algebra allow us to apply Tikhonov-like techniques within O(n d log(n)) arithmetic operations, where n d is the number of pixels of the reconstructed object. Extensive numerical experimentation concerning 2D images and strongly symmetric PSFs confirms the effectiveness of our proposal.
|Data di pubblicazione:||2008|
|Titolo:||The anti-reflective algebra: structural and computational analysis with application to image deblurring and denoising|
|Digital Object Identifier (DOI):||10.1007/s10092-008-0148-1|
|Codice identificativo ISI:||WOS:000259304300001|
|Codice identificativo Scopus:||2-s2.0-58449087816|
|Parole Chiave:||Boundary conditions - fast transforms and matrix algebras - re-blurring - Tikhonov-like regularization|
|Appare nelle tipologie:||Articolo su Rivista|