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Image Deblurring – A Case Study

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Sparse and Redundant Representations
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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.

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Further Reading

  1. 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.

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  4. 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.

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  9. 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.

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Correspondence to Michael Elad .

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Elad, M. (2010). Image Deblurring – A Case Study. In: Sparse and Redundant Representations. Springer, New York, NY.

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