Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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An Explicit Solution of EM Algorithm in Image Deblurring: Image Restoration without EM iterations

영상흐림보정에서 EM 알고리즘의 일반해: 반복과정을 사용하지 않는 영상복원

  • Kim, Seung-Gu (Department of Data & Information, Sangji University)
  • 김승구 (상지대학교 컴퓨터데이터정보학과)
  • Published : 2009.05.31
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Abstract

In this article, an explicit solution of the EM algorithm for the image deburring is presented. To obtain the restore image from the strictly iterative EM algorithm is quite time-consumed and impractical in particular when the underlying observed image is not small and the number of iterations required to converge is large. The explicit solution provides a quite reasonable restore image although it exploits the approximation in the outside of the valid area of image, and also allows to obtain the effective EM solutions without iteration process in real-time in practice by using the discrete finite Fourier transformation.

본 연구에서는 영상흐림보정를 위한 EM 알고리즘의 일반형 해를 제공한다. 주어진 관측영상의 크기가 크거나 많은 반복을 필요로 할 때, EM 알고리즘의 반복은 매우 오랜시간이 걸리며 비실용적이다. 본 연구에서는 복원 영상의 유효영역 밖에서 약간의 근사로부터 해를 일반형으로 나타내고, 이것을 이산형 유한 푸리에 변환을 이용하여 EM 알고리즘의 반복과정을 사용하지 않으면서 매우 유효한 복원영상을 즉시 계산하는 방법을 제공한다.

Keywords

References

  1. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum Likelihood from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society, Series B, 39, 1-38
  2. Hall, P. and Qui, P. (2007a). Blind deconvolution and deblurring in image analysis, Statistica Sinica, 17, 1483-1509
  3. Hall, P. and Qui, P. (2007b). Nonparametric estimation of a point spread function in multivariate problems, The Annals of Statistics, 35, 1512-1534 https://doi.org/10.1214/009053606000001442
  4. Jain, A. K. (1989). Fundamentals of Digital Image Processing, Prentice-Hall, New York
  5. Lee, S. (2008). A note on nonparametric density estimation for the deconvolution problem, Communications of the Korean Statistical Society, 15, 939-946 https://doi.org/10.5351/CKSS.2008.15.6.939
  6. McElroy, F. W. (1967). A necessary and sufficient condition that ordinary least squares estimators be best linear unbiased, Journal of American Statistical Association, 62, 1302-1304 https://doi.org/10.2307/2283779
  7. McLachlan, G. J. and Krishnan, T. (2008). The EM Algorithm and Extensions, John Wiley & Sons, New York
  8. Meng, X. -L. and van Dyk, D. A. (1997). The EM algorithm-an old folk-song sung to a fast new tune, Journal of the Royal Statistical Society, Series B, 59, 511-567 https://doi.org/10.1111/1467-9868.00082
  9. Meng, X. -L. and Rubin, D. B. (1994). On the global and componentwise rates of convergence of the EM algorithm, Linear Algebra and its Applications, 199, 413-425 https://doi.org/10.1016/0024-3795(94)90363-8
  10. Molina, R., Nunez, J., Cortijo, F. and Mateos, J. (2001). Image restoration in astronomy: A Bayesian prospective, In IEEE Signal Processing Magazine, 18, 11-29 https://doi.org/10.1109/79.916318
  11. Mona, A. and Kay, J. (1990). Edge preserving image restoration, Stochastic Models, Statistical Methods, and Algorithms in Image Analysis, Eds. Barone, P., Frigessi, A., and Piccioni, M., Springer-Verlag, 1-13
  12. Searle, S. R. (1982). Matrix Algebra Useful for Statistics, Wiley, New York
  13. Qui, P. (2008). A nonparametric procedure for blind image deblurring, Computational Statistics and Data Analysis, 52,4828-4841 https://doi.org/10.1016/j.csda.2008.03.027