Image Deblurring – A Case Study

  • Michael Elad


In this chapter we present an application of the Sparse-Land model to image deblurring, in order to demonstrate the applicative side of the above-discussed model and algorithms. As we show next, this long-studied problem can be handled quite effectively using the fundamentals of the model with hardly any changes. The content of this chapter follows closely with the work by M.A.T. Figueiredo and R.D. Nowak that appeared in ICIP 2005, and a later paper by M. Elad, B. Matalon, and M. Zibulevsky (2007). While there exists a more recent work that leads to somewhat improved results, the appeal in this work is the relative simplicity with which near-state-of-the-art results are obtained.


Noisy Image Haar Wavelet Blur Kernel Image Deconvolution Image Deblurring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Further Reading

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    J. Bioucas-Dias, Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors, IEEE Trans. on Image processing, 15(4):937–951, April 2006.CrossRefMathSciNetGoogle Scholar
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    K. Dabov, A. Foi, and K. Egiazarian, Image restoration by sparse 3D transformdomain collaborative filtering, Proc. SPIE Electronic Imaging ’08, no. 6812–07, San Jose, California, USA, January 2008.Google Scholar
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    M. Elad, B. Matalon, and M. Zibulevsky, On a Class of Optimization methods for Linear Least Squares with Non-Quadratic Regularization, Applied and Computational Harmonic Analysis, 23:346–367, November 2007.MATHCrossRefMathSciNetGoogle Scholar
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    M. Elad, B. Matalon, J. Shtok, and M. Zibulevsky, A wide-angle view at iterated shrinkage algorithms, SPIE (Wavelet XII) 2007, San-Diego CA, August 26–29, 2007.Google Scholar
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    M.A. Figueiredo and R.D. Nowak, An EM algorithm for wavelet-based image restoration, IEEE Trans. Image Processing, 12(8):906–916, 2003.CrossRefMathSciNetGoogle Scholar
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    M.A. Figueiredo, and R.D. Nowak, A bound optimization approach to waveletbased image deconvolution, IEEE International Conference on Image Processing - ICIP 2005, Genoa, Italy, 2:782–785, September 2005.Google Scholar
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    M.A. Figueiredo, J.M. Bioucas-Dias, and R.D. Nowak, Majorization-minimization algorithms for wavelet-based image restoration, IEEE Trans. on Image Processing, 16(12):2980–2991, December 2007.CrossRefMathSciNetGoogle Scholar
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    H. Takeda, S. Farsiu, and P. Milanfar, Deblurring using regularized locallyadaptive kernel regression, IEEE Trans. on Image Processing, 17(4):550–563, April 2008CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Computer Science DepartmentThe Technion – Israel Institute of TechnologyHaifaIsrael

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