The Journal of the Korea institute of electronic communication sciences (한국전자통신학회논문지)

Korea Institute of Electronic Communication Science (한국전자통신학회)
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An Extension of Unified Bayesian Tikhonov Regularization Method and Application to Image Restoration

통합 베이즈 티코노프 정규화 방법의 확장과 영상복원에 대한 응용

  • Yoo, Jae Hung (Dept. of Computer Engineering, Chonnam Nat. Univ.)
  • 류재흥 (전남대학교 컴퓨터공학과)
  • Received : 2019.12.15
  • Accepted : 2020.02.15
  • Published : 2020.02.29
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Abstract

This paper suggests an extension of the unified Bayesian Tikhonov regularization method. The unified method establishes the relationship between Tikhonov regularization parameter and Bayesian hyper-parameters, and presents a formula for obtaining the regularization parameter using the maximum posterior probability and the evidence framework. When the dimension of the data matrix is m by n (m >= n), we derive that the total misfit has the range of m ± n instead of m. Thus the search range is extended from one to 2n + 1 integer points. Golden section search rather than linear one is applied to reduce the time. A new benchmark for optimizing relative error and new model selection criteria to target it are suggested. The experimental results show the effectiveness of the proposed method in the image restoration problem.

본 논문은 통합 베이즈 티코노프 정규화 방법을 확장하는 것을 제시한다. 통합된 방법은 티코노프 정규화 모수와 베이즈 하이퍼 모수들의 관계를 정립하고 최대 사후 확률과 근거 프레임워크를 사용한 정규화 모수를 구하는 공식을 제시한다. 데이터 행렬의 차원이 m by n (m >= n)일 때, total misfit는 기존의 m에서 m ± n로 확장된다. 따라서 탐색 범위도 1에서 2n+1개의 정수로 확장된다. 선형 탐색보다는 황금분할 탐색으로 시간을 줄인다. 상대오차를 최적화하는 새로운 벤치마크를 제안하고 이를 목표로 하는 새 모델 선택 판정기준을 소개한다. 실험결과는 영상 복원 문제에 대하여 제안하는 방법의 효능을 보여준다.

Keywords

References

  1. H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems. Dordrecht: Kluwer Academic Publishers, 1996.
  2. S. Kim, "An image denoising algorithm for the mobile phone cameras," J. of the Korea Institute of Electronic Communication Sciences, vol. 9, no. 5, 2014, pp. 601-608. https://doi.org/10.13067/JKIECS.201.9.5.601
  3. R. C. Gonzalez and R. E. Woods, Digital Image Processing. Reading: Addison-Wesley, 1992.
  4. J. Yoo, "A Unified Bayesian Tikhonov Regularization Method for Image Restoration," J. of the Korea Institute of Electronic Communication Sciences, vol. 11, no. 11, 2016, pp. 1129-1134. https://doi.org/10.13067/JKIECS.2016.11.11.1129
  5. R. Duda and P. Hart, Pattern Classification and Scene Analysis. New York: John Wiley & Sons, 1973.
  6. D. J. C. MacKay, "Bayesian interpolation," Neural Computation, vol. 4, no. 3, 1992, pp. 415-445. https://doi.org/10.1162/neco.1992.4.3.415
  7. G. Golub, M. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics, vol. 21, no. 2, 1979, pp. 215-223. https://doi.org/10.1080/00401706.1979.10489751
  8. H. Akaike, "Statistical predictor identification." Ann. Inst. Statist. Math. vol. 22, 1970, pp. 203-217. https://doi.org/10.1007/BF02506337
  9. W. H. Press et al. Numerical Recipes: The Art of Scientific Computing. New York: Cambridge Univ. Press, 2007.
  10. J. Nagy, K. Palmer, and L. Perrone, "Iterative methods for image deblurring: a Matlab object oriented approach," Numerical Algorithms, vol. 36, no. 1, 2004, pp. 73-93. https://doi.org/10.1023/B:NUMA.0000027762.08431.64
  11. P. Hansen and D. O'Leary, "The use of the L-curve in the regularization of discrete ill-posed problems," Society for Industrial and Applied Mathematics J. on Scientific Computing, vol. 14, no. 6, 1993, pp. 1487-1503.
  12. V. Morozov, Methods for Solving Incorrectly Posed Problems. New York: Springer-Verlag, 1984.
  13. J. Yoo, "Self-Regularization Method for Image Restoration," J. of the Korea Institute of Electronic Communication Sciences, vol. 11, no. 1, 2016, pp. 45-52. https://doi.org/10.13067/JKIECS.2016.11.1.45
  14. Y. Kim, "A Study on Fractal Image Coding," J. of the Korea Institute of Electronic Communication Sciences, vol. 7, no. 3, 2012, pp. 559-566. https://doi.org/10.13067/JKIECS.2012.7.3.559
  15. C. Lee and J. Lee, "Implementation of Image Improvement using MAD Order Statistics for SAR Image in Wavelet Transform Domain," J. of the Korea Institute of Electronic Communication Sciences, vol. 9, no. 12, 2014, pp. 1381-1388. https://doi.org/10.13067/JKIECS.2014.9.12.1381
  16. S. Park, "Optimal QP Determination Method for Adaptive Intra Frame Encoding," J. of the Korea Institute of Electronic Communication Sciences, vol. 10, no. 9, 2015, pp. 1009-1018. https://doi.org/10.13067/JKIECS.2015.10.9.1009