Email this article 
Image Reconstruction via Classification Using Fourier Synthesis and Prior Information in Bayesian Analysis
(*) Corresponding author
DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)
Abstract
Fourier Synthesis inverse problem consists in reconstructing an image from the measured data which correspond to partial and noisy information of its Fourier Transform. This inverse problem is known to be nonlinear and ill-posed. It then needs to be regularized by introducing prior information. In this paper we propose two priors information. In the first prior information, we assume that the original image is composed by homogeneous regions, so in this case we propose the Hidden Markov Modeling dedicated to classification which is the most appropriate distribution for the image labels in a Bayesian framework. In the second prior information we assume that the noise is a Gaussian centered and in order to improve the quality of image reconstruction we introduce a total variation algorithm with a Bayesian analysis to regularize the solution.
Appropriate Markov Chain Monte Carlo algorithms are proposed to implement our approach. This method is applied on synthetics and real images
Copyright © 2014 Praise Worthy Prize - All rights reserved.
Keywords
References
Bracewell RN. The Fourier transform and its applications International Ed. MacGraw-Hill Int. 1986.
Denny Jr TS, Reeves SJ. In Computational Imaging IV.2006. p. 96-107.
Bojan BG, Andrew IM. A linear sampling approach to Inverse elastic scattering in piecewise- homogeneous domain. inverse problems 2007;23:1467-93
Shieh Hsin M, Byrne Charles L, Testorf Markus E, Fiddy Michael A. “ Iterative image reconstruction using prior Knowledge”. Journal of the optical society of America A 2006; 23(6): 1292-300
Alessio A, Kinahan P, PET image reconstruction. In: Henkin, et al., editors Nuclear medicine. 2nd ed. Philadelphia: Elsevier; 2006.
de Villiers GD, McNally B, pike ER. Positive solution to linear inverse problems. Inverse problems 1999; 15: 615.
O. Feron, Z. Chama and A. Mohammad-Djafari, “ Reconstruction Of piecewise homogenous images from Partial knowledge of their fourier transform”. American Institut of Physics (AIP) Conference Proceedings 735 (2004), 68–75.
Z. Chama, M.F. Belbachir and A. Mohammad-Djafari, phase Retrieval algorithm using Bayesian approach. AEU-International Journal of Electronics and Communications, Elsevier, 61(2007), 66–68.
J. Bioucas-Dias, M. Figueiredo and J. Oliveira, Adaptive total- variation image deconvolution: A majorization-minimization approach. Proceedings of EUSIPCO’ 2006, Florence, Italy, September 2006
Wu, Q., Wang, K., Zuo, W., Total variation-based image restoration using I-divergence, (2013) International Review on Computers and Software (IRECOS), 8 (2), pp. 668-672.
Fessler Jeffrey, Noll Douglas C. Iterative image reconstructi- on in MRI with separate magnitude and phase Regularization. In: IEEE International Symposuim on Biomedical Imaging. 2004.p. 209-12.
Olivier Fron, Ali Mohammad-Djafari. Image fusion and unsu- pervised segmentation using a HMM and MCMC algorithms. Journal of Electronic Imaging 2005; 14(May):023014.
Jianxin Han, Hatzinakos D. Joint blind deconvolution, fusion and classification of multi-frame imagery. In: Canadian conference on Electrical and computer Engineering, Vol.4, May. 2004. P.2061-4
Mclachlan GJ, Peel D. Finite Mixture models. New York:A Wiley -Interscience publication; 2000.
S. Osher, L. Rudin and E. Fatemi, Nonlinear total variation based noise removal algorithms. Physica D. 60 (1992), 259–268.
G. Archer and D. Titterington, “On some Bayesian/ regularization methods for image restoration” IEEE Trans. On Image processing , vol. 4, pp. 989 - 995, 1995.
N. Galatsanos and A. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. On Image Processing, vol. 1, pp. 322-336, 1992.
N. Galatsanos, V. Mesarovic, R. Molina, J. Mateos, and A. Katsaggelos, “Hyper-parameter estimation using gamma hyper- priors in image restoration from partially-known blurs” optical Engineering, vol. 41, pp. 1845-1854, 2002.
R. Molina, A. Katsaggelos, and J. Mateos, “Bayesian and Regularization methods for hyper-parameter estimation in image restoration,” IEEE Trans. Image Processing, vol. 8, pp. 231-246. 1999.
J. Besag, “On the statistical analysis of dirty pictures”, Journal of the Royal Statistical Society B, vol. 48, pp. 259- 302, 1986.
A. Mohammad-Djafari, “A full Bayesian approach for inverse problems” in Maximum Entropy and Bayesian Method, K. Hanson and R. Silver (Eds), Kluwer, 1996.
J. Bioucas-Dias, M. Figueiredo and J. Oliveira, “Adaptive total- Variation image deconvolution: Amajorization-minimisation approach”. Proceedings of EUSIPCO’ 2006, Florence, Italy, September 2006.
Z. Chama, F. Humblot and A. Mohamad-Djafari, Image recovery from the magnitude of the fourier transform using a Gaussian mixture with hidden potts-markov model. American Institut of Physics (AIP) Conference Proceedings 803 (2005),239–246.
O. Feron, Z. Chama and Ali. Mohammad-Djafari “ Reconstruction of piecewise images from partial knowledge of their fourier transform”. American Institut of Physics (AIP) Conference Proceedings 735 (2004), 68–75.
Z. Chama , B. Mansouri,M.Anani, A. Mohammad-Djafari, Image recovery from Fourier domaine measurements via classification using Bayesian approach and total variation regularization. Int J of Electronics and Communication (AEU) (2012).doi: 10.01016 j.aeue.2012.03.008.
Refbacks
- There are currently no refbacks.
Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize
