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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 Zheng-Jian Bai.

A Fast Alternating Minimization Algorithm for Total Variation Deblurring Without Boundary Artifacts, Z. J. Bai, D. Cassani, M. Donatelli, and S. Serra-Capizzano, J. Math. Anal. Appl., 415 (2014), pp. 373–393.


2. ANTIREFLECTIVE BOUNDARY CONDITIONS (AR-BCs)

2.1 FAST MATRIX COMPUTATIONS

In the case of symmetric PSF, imposing AR-BCs 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

  1. Spectral analysis of the anti-reflective algebra, A. Arico', M. Donatelli, and S. Serra-Capizzano, Linear Algebra Appl., 428 (2008), pp. 657--675.
  2. The Anti-Reflective 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 AR-BCs.

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 AR-BCs. For more detalis see:

Improved image deblurring with anti-reflective boundary conditions and re-blurring, M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, Inverse Problems, 22 (2006) pp. 2035--2053.