Parameter estimation in TV image restoration using variational distribution approximation

IEEE Transactions on Image Processing

Volumn 17, Issue 3, 2008, Pages 326-339

  Babacan, S Derin ^a   Molina, Rafael ^b   Katsaggelos, Aggelos K ^a  

^a Northwestern University   (United States)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

Bayesian methods; Image restoration; Parameter estimation; Total variation (TV); Variational methods

Indexed keywords

ALGORITHMS; PARAMETER ESTIMATION; TELEVISION PICTURE QUALITY;

BAYESIAN METHODS; TOTAL VARIATION; VARIATIONAL METHODS;

IMAGE RECONSTRUCTION;

ALGORITHM; ARTICLE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; STATISTICAL MODEL; TELEVISION; VIDEORECORDING;

ALGORITHMS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MODELS, STATISTICAL; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; TELEVISION; VIDEO RECORDING;

EID: 40849120186     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2007.916051     Document Type: Article

References (42)

1. S. D. Babacan, R. Molina, and A. K. Katsaggelos, "Total variation image restoration and parameter estimation using variational posterior distribution approximation," presented at the Int. Conf. Image Processing, San Antonio, TX, Sep. 2007.
2. A. K. Katsaggelos, Ed., Digital Image Restoration. New York: Springer-Verlag, 1991, vol. 23.
3. M. R. Banham and A. K. Katsaggelos, "Digital image restoration," IEEE Signal Process. Mag., vol. 14, no. 2, pp. 24-41, Mar. 1997.
4. P. Sarder and A. Nehorai, "Deconvolution methods for 3D fluorescence microscopy images: An overview," IEEE Signal Process. Mag., vol. 23, no. 3, pp. 32-45, May 2006.
5. T. F. Chan and J. Shen, Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. Philadelphia, PA: SIAM, 2005.
6. L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, pp. 259-268, 1992.
7. A. B. Hamza, H. Krim, and G. B. Unal, "Unifying probabilistic and variational estimation," IEEE Signal Process. Mag., vol. 19, no. 9, pp. 37-47, Sep. 2002.
8. T. F. Chan, S. Esedoglu, F. Park, and A. Yip, "Recent developments in total variation image restoration," in Handbook of Mathematical Models in Computer Vision, N. Paragios, Y. Chen, and O. Faugeras, Eds. New York: Springer Verlag, 2005.
9. M. Bertalmio, V. Caselles, B. Rougé, and A. Solé, "TV based image restoration with local constraints," J. Sci. Comput., vol. 19, no. 1-3, pp. 95-122, Dec. 2003.
10. J. Bioucas-Dias, M. Figueiredo, and J. Oliveira, "Adaptive total-variation image deconvolution: A majorization-minimization approach," presented at the EUSIPCO, Florence, Italy, Sep. 2006.
11. J. Bioucas-Dias, M. Figueiredo, and J. Oliveira, "Total-variation image deconvolution: A majorization-minimization approach," presented at the ICASSP, Toulouse, France, May 2006.
12. R. Molina, A. K. Katsaggelos, and J. Mateos, "Bayesian and regularization methods for hyperparameter estimation in image restoration," IEEE Trans. Image Process., vol. 8, no. 2, pp. 231-246, Feb. 1999.
13. J. Mateos, A. Katsaggelos, and R. Molina, "A Bayesian approach to estimate and transmit regularization parameters for reducing blocking artifacts," IEEE Trans. Image Process., vol. 9, no. 7, pp. 1200-1215, Jul. 2000.
14. N. P. Galatsanos, V. Z. Mesarovic, R. Molina, A. K. Katsaggelos, and J. Mateos, "Hyperparameter estimation in image restoration problems with partially-known blurs," Opt. Eng., vol. 41, no. 8, pp. 1845-1854, Aug. 2002.
15. R. Molina, J. Mateos, and A. Katsaggelos, "Blind deconvolution using a variational approach to parameter, image, and blur estimation," IEEE Trans. Image Process., vol. 15, no. 12, pp. 3715-3727, Dec. 2006.
16. R. Molina, "On the hierarchical Bayesian approach to image restoration. Applications to astronomical images," IEEE Trans. Pattern Anal. Mach. Intell., vol. 16, no. 11, pp. 1122-1128, Nov. 1994.
17. N. P. Galatsanos, V. Z. Mesarovic, R. Molina, and A. K. Katsaggelos, "Hierarchical Bayesian image restoration for partially-known blur," IEEE Trans. Image Process., vol. 9, no. 8, pp. 1784-1797, Aug. 2000.
18. C. Andrieu, N. de Freitas, A. Doucet, and M. I. Jordan, "An introduction to MCMC for machine learning," Mach. Learn., vol. 50, no. 1-2, pp. 5-43, Jan. 2003.
19. J. Miskin, "Ensemble learning for independent component analysis," Ph.D. dissertation, Astrophysics Group, Univ. Cambridge, Cambridge, U.K., 2000.
20. M. J. Beal, "Variational algorithms for approximate bayesian inference," Ph.D. dissertation, The Gatsby Computational Neuroscience Unit, Univ. College London, London, U.K., 2003.
21. V. Smidl and A. Quinn, The Variational Bayes Method in Signal Processing. New York: Springer Verlag, 2005.
22. C. M. Bishop, Pattern Recognition and Machine Learning. New York: Springer, 2006.
23. M. I. Jordan, Z. Ghahramani, T. S. Jaakola, and L. K. Saul, "An Introduction to variational methods for graphical models," in Learn. Graph. Models. Cambridge, MA: MIT Press, 1998, pp. 105-162.
24. S. Kullback Information Theory and Statistics. New York: Dover, 1959.
25. C. M. Bishop and M. E. Tipping, "Variational relevance vector machine," in Proc. 16th Conf. Uncertainty in Articial Intelligence 2000, pp. 46-53.
26. J. W. Miskin and D. J. C. MacKay, "Ensemble learning for blind image separation and deconvolution," in Advances in Independent Component Analysis, M. Girolami, Ed. New York: Springer-Verlag, July 2000.
27. 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, Aug. 2004.
28. J. O. Berger, Statistical Decision Theory and Bayesian Analysis. New York: Springer Verlag, 1985, ch. 3 and 4.
29. K. Lange, "Optimization," in Springer Texts in Statistics. NewYork: Springer-Verlag, 2004.
30. T. S. Jaakkola and M. I. Jordan, "Bayesian parameter estimation via variational methods," Statist. Comput., vol. 10, no. 1, pp. 25-37, 2000.
31. C. Bishop and M. Svensen, "Bayesian hierarchical mixtures of experts," in Proc. 19th Annu. Conf. Uncertainty in Artificial Intelligence, San Francisco, CA, 2003, pp. 57-64.
32. C. M. Bishop, Pattern Recognition and Machine Learning. New York: Springer-Verlag, 2006.
33. G. L. Anderson and A. N. Netravali, "Image restoration based on a subjective criterion," IEEE Trans. Syst., Man, Cybern., vol. SMC-6, no. 6, pp. 845-853, Dec. 1976.
34. A. K. Katsaggelos and M. G. Kang, "A spatially adaptive iterative algorithm for the restoration of astronomical images," Proc. Int. J. Imag. Syst. Technol., vol. 6, no. 4, pp. 305-313, 1995.
35. A. K. Katsaggelos, K. T. Lay, and N. P. Galatsanos, "A general framework for frequency domain multi-channel signal processing," IEEE Trans. Image Process., vol. 2, no. 3, pp. 417-420, Jul. 1993.
36. J. Besag, "On the statistical analysis of dirty pictures," J. Roy. Statist. Soc. B, vol. 48, no. 3, pp. 259-302, 1986.
37. B. D. Ripley, Spatial Statistics. New York: Wiley, 1981, pp. 88-90.
38. R. H. Chan, T. F. Chan, and C.-K. Wong, "Cosine transform based preconditioners for total variation deblurring," IEEE Trans. Image Process., vol. 8, no. 10, pp. 1472-1478, Oct. 1999.
39. C. R. Vogel and M. E. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Process. vol. 7, no. 6, pp. 813-824, Jun. 1998.
40. T. F. Chan, N. Ng, A. Yau, and A. Yip, "Superresolution image reconstruction using fast inpainting algorithms," Appl. Comput. Harmon. Anal., vol. 23, no. 1, pp. 3-24, July 2007.
41. M. K. Ng, H. Shen, E. Y. Lam, and L. Zhang, "A total variation regularization based super-resolution reconstruction algorithm for digital video," EURASIP J. Adv. Signal Process., no. 74585, 2007.
42. J. Nocedal and S. J. Wright, Numerical Optimization. New York: Springer-Verlag, 1999.