Blind Image Deconvolution by Neural Recursive Function Approximation
This work explores blind image deconvolution by recursive function approximation based on supervised learning of neural networks, under the assumption that a degraded image is linear convolution of an original source image through a linear shift-invariant (LSI) blurring matrix. Supervised learning of neural networks of radial basis functions (RBF) is employed to construct an embedded recursive function within a blurring image, try to extract non-deterministic component of an original source image, and use them to estimate hyper parameters of a linear image degradation model. Based on the estimated blurring matrix, reconstruction of an original source image from a blurred image is further resolved by an annealed Hopfield neural network. By numerical simulations, the proposed novel method is shown effective for faithful estimation of an unknown blurring matrix and restoration of an original source image.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333965Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1661
 L. Bar, N. Sochen and N. Kiryati, "Semi-blind image restoration via Mumford-Shah regularization," IEEE Trans. Image Process., vol. 15, no. 2, pp. 483--493, Feb 2006.
 D. Kundur and D. Hatzinakos, "Blind image deconvolution," IEEE Trans. Signal Process. Mag., vol. 13, no. 3, pp. 43--64, Mar. 1996.
 T. E. Bishop, S. D. Babacan, B. Amizic, A. K. Katsaggelos, T. Chan, and R. Molina, "Blind image deconvolution: Problem formulation and existing approaches," in Blind Image Deconvolution: Theory and Applications, P. Campisi and K. Egiazarian, Eds. Boca Raton, FL: CRC, ch. 1, 2007.
 Nan Xie and Henry Leung, Member, "IEEE Blind Equalization Using a Predictive Radial Basis Function Neural Network," IEEE Trans. Neural Networks., vol. 16, no. 3, May 2005.
 J. M. Wu and C. S. Lian, "Blind Deconvolution by Supervised Learning of Neural Networks," Master thesis, Department of Applied Mathematics, National Dong Hwa University, Jul. 2008.
 S. Kullback, "Information Theory and Statistics," New York: Dover, 1959.
 A. C. Likas and N. P. Galatsanos, "A variational approach for Bayesian blind image deconvolution," IEEE Trans. Signal Process., vol. 52, no. 8, pp. 2222--2233, 2004.
 K. Z. Adami, "Variational methods in Bayesian deconvolution," in Proc. PHYSTAT ECONF, 2003, vol. CO30908, p. TUGT002.
 S. D. Babacan, R. Molina and A. K. Katsaggelos, "Variational Bayesian Blind Deconvolution Using a Total Variation Prior," IEEE Trans. Image Process., vol. 18, no. 1, Jan. 2009.
 R. Jirik and T. Taxt, "Two-dimensional blind Bayesian deconvolution of medical ultrasound images," IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency Control., vol 55, no 10, pp. 2140 - 2153, Oct. 2008.
 D. G. Tzikas, A. C. Likas and N. P. Galatsanos, "Variational Bayesian Sparse Kernel-Based Blind Image Deconvolution With Student's-t Priors," IEEE Trans. Image Process., vol. 18, no. 4, pp. 753 - 764, Apr. 2009.
 J. M. Wu, "Annealing by Two Sets of Interactive Dynamics," IEEE Trans. Systems, Man, and Cybernetics, Part B., vol. 34, no. 3, pp. 1519 - 1525. Jun. 2004.
 J. J. Hopfield and D. W. Tank, "Neural computation of decisions in optimizationproblems," Biol. Cybern., vol. 52, pp. 141, 1985.
 J. B. MacQueen, (1967) . "Some Methods for classification and Analysis of Multivariate Observations" in Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability. 1: 281--297, University of California Press. MR0214227. Zbl 0214.46201. Retrieved on 2009-04-07.
 Gunnar R├ñtsch, "A (Partial) Documentation of RBF & AdaBoostReg Software Packages."
 M. N├©rgaard, O. Ravn, N. K. Poulsen and L. K. Hansen. "Neural Networks for Modelling and Control of Dynamic Systems," London, U.K.:Springer-Verlag, 2000.
 Matlab toolbox "Deblurring Images Using the Blind Deconvolution Algorithm."