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

한국전자통신학회 (Korea Institute of Electronic Communication Science)
권호 표지
DOI QR코드

DOI QR Code

영상 복원을 위한 통합 베이즈 티코노프 정규화 방법

A Unified Bayesian Tikhonov Regularization Method for Image Restoration

  • 류재흥 (전남대학교 컴퓨터공학과)
  • Yoo, Jae-Hung (Dept. of Computer Engineering, Chonnam Nat. Univ.)
  • 투고 : 2016.11.01
  • 심사 : 2016.11.24
  • 발행 : 2016.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문은 영상 복원 문제에 대한 정규화 모수를 찾는 새로운 방법을 제시한다. 사전 정보가 없으면 티코노프(Tikhonov) 정규화 모수를 선택하기 위한 일반화된 교차 검증법이나 L자형 곡선 검정 등의 별도의 최적화 함수가 필요하다. 본 논문에서는 티코노프 정규화에 대한 통합된 베이즈 해석을 소개하고 영상 복원 문제에 적용한다. 티코노프 정규화 모수와 베이즈 하이퍼 모수들의 관계를 정립하고 최대 사후 확률과 근거 프레임워크를 사용한 정규화 모수를 구하는 공식을 제시한다. 실험결과는 제안하는 방법의 효능을 보여준다.

This paper suggests a new method of finding regularization parameter for image restoration problems. If the prior information is not available, separate optimization functions for Tikhonov regularization parameter are suggested in the literature such as generalized cross validation and L-curve criterion. In this paper, unified Bayesian interpretation of Tikhonov regularization is introduced and applied to the image restoration problems. The relationship between Tikhonov regularization parameter and Bayesian hyper-parameters is established. Update formular for the regularization parameter using both maximum a posteriori(: MAP) and evidence frameworks is suggested. Experimental results show the effectiveness of the proposed method.

키워드

참고문헌

  1. R. Gonzalez and R. Woods, Digital Image Processing. Reading, MA: Addison-Wesley, 1992.
  2. H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems. Dordrecht: Kluwer Academic Publishers, 1996.
  3. 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
  4. 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
  5. 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.
  6. V. Morozov, Methods for Solving Incorrectly Posed Problems. New York: Springer-Verlag, 1984.
  7. 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
  8. R. Duda and P. Hart, Pattern Classification and Scene Analysis. New York: John Wiley & Sons, 1973.
  9. D. MacKay, "Bayesian interpolation," Neural Computation, vol. 4, no. 3, 1992, pp. 415-445. https://doi.org/10.1162/neco.1992.4.3.415
  10. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, Philadelphia: Society for Industrial and Applied Mathematics, 1998.
  11. 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
  12. 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
  13. 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
  14. 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