BLIND IMAGE DEBLURRING WITH UNKNOWN BOUNDARIES USING
THE ALTERNATING DIRECTION METHOD OF MULTIPLIERS
(Abstract, data and MATLAB code)
Abstract (of ):
Blind image deblurring (BID) is an ill-posed inverse problem, typically solved by imposing some form of regularization (prior knowledge) on the unknown blur and original image. A recent approach, although not requiring prior knowledge on the blurring filter, achieves state-of-the-art performance for a wide range of real-world BID problems. We propose a new version of that method, in which both the optimization problems with respect to the unknown image and with respect to the unknown blur are solved by the alternating direction method of multipliers (ADMM) – an optimization tool that has recently sparked much interest for solving inverse problems, namely due to its modularity and state-of-the-art speed. Our approach also handles seamlessly the realistic case of blind deblurring with unknown boundary conditions. Experiments with synthetic and real blurred images show the competitiveness of the proposed method, both in terms of speed and restoration quality.
In our previous work [4,5], we proposed computing the quality of BID methods using an adapted version of the "improvement in SNR" (ISNR) measure, which should be invariant under variations that do not affect the quality of the restored images; specifically, this measure should be invariant to: 1) any affine transformation of the intensity scale; 2) small translations (in opposite directions) of the estimated image and blurring filter. The MATLAB code for this adapted ISNR measure is
also included in the code available below.
As stopping criteria for the BID method of , we can use those based on measures of residual whiteness, which we have proposed in [2,3] (see also this webpage). The MATLAB code for these measures is also included in the package available below.
References on This BID Method:
 M. S. C. Almeida and M. A. T. Figueiredo,, "Blind Image Deblurring with Unknown Boundaries Using the Alternating Direction Method of Multipliers", IEEE International Conf. on Image Processing – ICIP’2013, Melbourne, Australia, September, 2013.
References on Measures of Whiteness for stopping criteria (webpage here):
 M. S. C. Almeida and M. A. T. Figueiredo, “Stopping Criteria for Iterative Blind and Non-Blind Image Deblurring Algorithms Based on Residual Whiteness Measures”, IEEE Trans Image Processing, vol. 22, nº7, pp.2751-63, 2013. (Abstract and MATLAB code)
 M. S. C. Almeida and M. A. T. Figueiredo, “New stopping criteria for iterative blind image deblurring based on residual whiteness measures”, IEEE Workshop on Statistical Signal Processing – SSP’2011, Nice, France, 2011.
References on the Previous BID Approach (webpage here):
 M. S. C. Almeida and L. B. Almeida, “Blind deblurring of natural images”, IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP’ 2008, March, Las Vegas, 2008. (PDF, Poster)
If you find any bug, please report it to me: M. S. C. Almeida. Thank you!
LICENSE: This code is copyright of Mário A. T. Figueiredo and Mariana S.C. Almeida. Free permission is given for their use for nonprofit research purposes. Any other use is prohibited, unless a license is previously obtained.
This package is compressed with 7-zip.
ACKNOWLEDGEMENTS: This work was partially supported by Fundação para a Ciência e Tecnologia (FCT), under grants PTDC/EEA-TEL/104515/2008, PEst-OE/EEI/LA0008/2013, PTDC/EEI-PRO/1470/2012, and the fellowship SFRH/BPD/69344/2010.