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Bayesian image superresolution and hidden variable modeling

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Abstract

Superresolution is an image processing technique that estimates an original high-resolution image from its low-resolution and degraded observations. In superresolution tasks, there have been problems regarding the computational cost for the estimation of high-dimensional variables. These problems are now being overcome by the recent development of fast computers and the development of powerful computational techniques such as variational Bayesian approximation. This paper reviews a Bayesian treatment of the superresolution problem and presents its extensions based on hierarchical modeling by employing hidden variables.

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References

  1. S. Borman and R. L. Stevenson, Spatial resolution enhancement of low-resolution image sequences: A comprehensive review with directions for future research, Technical Report, Dept. of Electrical Engineering, University of Notre Dame, 1998.

  2. S. C. Park, M. K. Park, and M. G. Kang, Super-resolution image reconstruction: A technical overview, IEEE Signal Process. Mag., 2003, 20(3): 21–36.

    Article  Google Scholar 

  3. S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, Advances and challenges in super-resolution, Int. J. Imag. Syst. Tech., 2004, 14(2): 47–57.

    Article  Google Scholar 

  4. A. K. Katsaggelos, R. Molina, and J. Mateos, Super Resolution of Images and Video, Morgan & Claypool, San Rafael, CA, 2007.

    Google Scholar 

  5. W. T. Freeman, T. R. Jones, and E. C. Pasztor, Example-based super-resolution, IEEE Comput. Graphics Appl., 2002, 22(2): 56–65.

    Article  Google Scholar 

  6. M. E. Tipping and C. M. Bishop, Bayesian image super-resolution, in Advances in Neural Information Processing Systems (NIPS) 15 (eds. by S. Becker, S. Thrun, and K. Obermayer), MIT Press, Cambridge, MA, 2003, 1279–1286.

    Google Scholar 

  7. A. Kanemura, S. Maeda, and S. Ishii, Edge-preserving Bayesian image superresolution based on compound Markov random fields, in Proc. International Conference on Artificial Neural Networks (ICANN) (ed. by J. Marques de Sá), LNCS 4669, Springer, 2007, II-611-620.

  8. A. Kanemura, S. Maeda, and S. Ishii, Image superresolution under spatially structured noise, Proc. IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), 2007, 279–284.

  9. W. Fukuda, S. Maeda, A. Kanemura, and S. Ishii, Bayesian image superresolution under moving occlusion (in Japanese), in IEICE Technical Report, 2008, 107(542): 237–242.

    Google Scholar 

  10. R. Y. Tsai and T. S. Huang, Multiframe image restoration and registration, in Advances in Computer Vision and Image Processing, JAI Press, Greenwich, CT, 1984, 1: 317–339.

    Google Scholar 

  11. M. Irani and S. Peleg, Improving resolution by image registration, CVGIP: Graph. Model. Im., 1991, 53(3): 231–239.

    Article  Google Scholar 

  12. H. Stark and P. Oskoui, High resolution image recovery from image-plane arrays, using convex projections, J. Opt. Soc. Am. A, 1989, 6: 1715–1726.

    Article  Google Scholar 

  13. R. R. Schultz and R. L. Stevenson, Extraction of high-resolution frames from video sequences, IEEE Trans. Image Process., 1996, 5(6): 996–1011.

    Article  Google Scholar 

  14. S. Z. Li, Markov Random Field Modeling in Image Analysis, Springer, Tokyo, 2001.

    MATH  Google Scholar 

  15. G. Winkler, Image Analysis, Random Fields, and Markov Chain Monte Carlo Methods (2nd ed.), Springer, Heidelberg, 2003.

    MATH  Google Scholar 

  16. R. C. Hardie, K. J. Barnard, and E. E. Armstrong, Joint MAP registration and high-resolution image estimation using a sequence of undersampled images, IEEE Trans. Image Process., 1997, 6(12): 1621–1633.

    Article  Google Scholar 

  17. C. Bouman and K. Sauer, A generalized Gaussian image model for edge-preserving MAP estimation, IEEE Trans. Image Process., 1993, 2(3): 296–310.

    Article  Google Scholar 

  18. S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, Fast and robust multiframe super resolution, IEEE Trans. Image Process., 2004, 13(10): 1327–1344.

    Article  Google Scholar 

  19. N. A. Woods, N. P. Galatsanos, and A. K. Katsaggelos, Stochastic methods for joint registration, restoration, and interpolation of multiple undersampled images, IEEE Trans. Image Process., 2006, 15(1): 201–213.

    Article  MathSciNet  Google Scholar 

  20. A. Rosenfeld and A. C. Kak, Digital Picture Processing (2nd ed.), Academic Press, New York, 1976.

    Google Scholar 

  21. L. C. Pickup, D. P. Capel, S. J. Roberts, and A. Zisserman, Bayesian methods for image superresolution, Comput. J., 2007, bxm091, Advance Access.

  22. A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Stat. Soc. B, 1977, 39(1): 1–38.

    MATH  MathSciNet  Google Scholar 

  23. R. M. Neal and G. E. Hinton, A view of the EM algorithm that justifies incremental, sparse, and other variants, in Learning in Graphical Models (ed. by M. I. Jordan), Kluwer Academic Press, Dordrecht, 1998, 355–368.

    Google Scholar 

  24. C. M. Bishop, Pattern Recognition and Machine Learning, Springer, New York, 2006.

    Book  MATH  Google Scholar 

  25. S. Kullback, Information Theory and Statistics, John Wiley and Sons, New York, 1959, (Reprinted by Dover, 1997).

    MATH  Google Scholar 

  26. S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell., 1984, PAMI-6(6): 721–741.

    Article  Google Scholar 

  27. F. C. Jeng and J. W. Woods, Compound Gauss-Markov random fields for image estimation, IEEE Trans. Signal Process., 1991, 39(3): 683–697.

    Article  Google Scholar 

  28. F. C. Jeng and J. W. Woods, Simulated annealing in compound Gaussian random fields, IEEE Trans. Inf. Theory, 1990, 36(1): 94–107.

    Article  MATH  MathSciNet  Google Scholar 

  29. M. I. Jordan, Z. Ghahramani, T. S. Jaakkola, and L. K. Saul, An introduction to variational methods for graphical models, Mach. Learn., November 1999, 37(2): 183–233.

    Article  MATH  Google Scholar 

  30. C. M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, New York, 1995.

    Google Scholar 

  31. J. A. Nelder and R. Mead, A simplex method for function minimization, Comput. J., 1965, 7: 308–313.

    MATH  Google Scholar 

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Correspondence to Atsunori Kanemura.

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This type of superresolution is in particular called multiframe superresolution or reconstruction-based superresolution. There is another type of superresolution called example-based superresolution[5], which estimates a high-resolution image from only one image rather than from multiple images, based on a database developed in advance. Example-based methods constitute another large class but they are beyond the scope of this article.

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Kanemura, A., Maeda, Si., Fukuda, W. et al. Bayesian image superresolution and hidden variable modeling. J Syst Sci Complex 23, 116–136 (2010). https://doi.org/10.1007/s11424-010-9277-0

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  • DOI: https://doi.org/10.1007/s11424-010-9277-0

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