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.

The anti-reflective algebra: structural and computational analysis with application to image deblurring and denoising

DONATELLI, MARCO;SERRA CAPIZZANO, STEFANO
2008

Abstract

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.
Boundary conditions - fast transforms and matrix algebras - re-blurring - Tikhonov-like regularization
Aricò, A.; Donatelli, Marco; SERRA CAPIZZANO, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11383/9442
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