

The following software
is developed only for research purpose and the
author is not responsible for its incorrect use.
The code was developed using Matlab 7.0.
This work has been partially supported by MIUR,
grant numbers 2004015437, 2006017542, and
20083KLJEZ.
1. FTVd WITHOUT BOUNDARY ARTIFACTS
This Matlab Toolbox uses a continuous version of the
FTVd algorithm in [Wang et al. SIAM J. Imaging Sci.,
1 (2008), pp. 248–272] to deal with boundary
artifacts (Matlab
Code). The author of this package is ZhengJian
Bai.
A Fast Alternating Minimization Algorithm for
Total Variation Deblurring Without Boundary
Artifacts, Z. J. Bai, D. Cassani, M.
Donatelli, and S. SerraCapizzano, J. Math. Anal.
Appl., 415 (2014), pp. 373–393.
2. ANTIREFLECTIVE BOUNDARY CONDITIONS (ARBCs)
2.1 FAST MATRIX COMPUTATIONS
In the case of symmetric PSF,
imposing ARBCs the associated matrix has a
special structure related to the discrete sine
transform. Such property is used in the AR Matlab
package (download). It
extends the HNO
package which should be uploaded and be
accessible to MATLAB, even if it is not necessary.
This package is done in collaboration with Antonio
Aric̣.
References
 Spectral analysis of the antireflective
algebra, A. Arico', M. Donatelli, and S.
SerraCapizzano, Linear Algebra Appl., 428
(2008), pp. 657675.
 The AntiReflective Transform and
Regularization by Filtering, A. Aric̣, M.
Donatelli, J. Nagy, and S. Serra Capizzano,
Numerical Linear Algebra in Signals, Systems,
and Control., Lecture Notes in Electrical
Engineering, Springer Verlag, Vol. 80 (2011) pp.
1–21.
2.1 EXTENSION OF RESTORETOOLS
The following two functions
extend the matrix vector product of the free
Matlab toolbox
RestoreTools, developed by J. Nagy's group,
adding the ARBCs.
Download and
replace:
 mtimes.m
(...\RestoreTools\Classes\@psfMatrix\)
 padarray.m
(...\RestoreTools\Classes\@psfMatrix\private\)
The function padarray
extend the previous one adding the antisymmetric
pad, while in mtimes is added the antireflexive
type of BCs. In this way it is possible to use
the iterative regularizing methods in
RestoreTools imposing ARBCs. For more detalis
see:
Improved image deblurring with antireflective
boundary conditions and reblurring, M.
Donatelli, C. Estatico, A. Martinelli, and S.
SerraCapizzano, Inverse Problems, 22 (2006) pp.
20352053.


