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

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

DOI QR Code

Self-Regularization Method for Image Restoration

영상 복원을 위한 자기 정규화 방법

  • Yoo, Jae-Hung (Dept. of Computer Engineering, Chonnam Nat. Univ.)
  • 류재흥 (전남대학교 컴퓨터공학과)
  • Received : 2015.12.09
  • Accepted : 2016.01.24
  • Published : 2016.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper suggests a new method of finding regularization parameter for image restoration problems. Wiener filter requires priori information such that power spectrums of original image and noise. Constrained least squares restoration also requires knowledge of the noise level. 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, self-regularization method that connects bias term of augmented linear system and smoothing term of Tikhonov regularization is introduced in the frequency domain and applied to the image restoration problems. Experimental results show the effectiveness of the proposed method.

본 논문은 영상 복원 문제에 대한 정규화 모수를 찾는 새로운 방법을 제시한다. 위너 필터(Wiener filter)는 원본 영상과 잡음의 파워 스펙트럼 등의 사전 정보를 요구한다. 제약된 최소자승 복원 역시 노이즈 수준에 대한 지식을 요구한다. 사전 정보가 없으면 티코노프(Tikhonov) 정규화 모수를 선택하기 위한 일반화된 교차 검증법이나 L자형 곡선 검정 등의 별도의 최적화 함수가 필요하다. 본 논문에서는 주파수 영역에서 선형 시스템의 바이어스 항목과 티코노프 정규화 시스템의 평활화 항목을 연결하는 자기 정규화 방법을 제안하고 영상 복원 문제에 적용한다. 실험결과는 제안하는 방법의 효능을 보여준다.

Keywords

References

  1. R. C. Gonzalez and R. E. 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. F. Bauer and M. Lukas, "Comparing parameter choice methods for regularization of ill-posed problems," Mathematics and Computers in Simulation vol. 81, no. 9, 2011, pp. 1795-1841. https://doi.org/10.1016/j.matcom.2011.01.016
  5. 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
  6. 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.
  7. V. Morozov, Methods for Solving Incorrectly Posed Problems. New York: Springer-Verlag, 1984.
  8. A. Bouhamidi and K. Jbilou, "Sylvester Tikhonov-regularization methods in image restoration," J. of Computational and Applied Mathematics, vol. 206, no. 1, 2007, pp. 86-98. https://doi.org/10.1016/j.cam.2006.05.028
  9. J. Jeong, "A new learning methodology for support vector machine and regularization RBF neural network," Master's Thesis, Chonnam National University, Feb. 2002.
  10. J. Yoo, "Automation of model selection through neural networks learning," Proc. Korea Fuzzy Logic and Intelligent Systems, Fall Conf. vol. 14, no. 2, Changwon, Korea, Oct., 2004, pp. 314-316.
  11. R. Duda and P. Hart, Pattern Classification and Scene Analysis. New York: John Wiley & Sons, 1973.
  12. A. Papoulis, Probability, Random Variables, and Stochastic Processes. 3rd edition, New York: McGraw-Hill, 1991.
  13. S. Haykin, Adaptive Filter Theory. 3rd edition, Upper Saddle River, NJ: Prentice Hall, 1996.
  14. B. Widrow and S. Stearns, Adaptive Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1985.
  15. O. Kwon, "The bi-directional least mean square algorithm and its application to echo cancellation," J. of the Korea Institute of Electronic Communication Sciences, vol. 9, no. 12, 2014, pp. 1337-1344. https://doi.org/10.13067/JKIECS.2014.9.12.1337
  16. Y. Han, "Interference cancellation system in repeater using adaptive algorithm with step sizes," J. of the Korea Institute of Electronic Communication Sciences, vol. 9, no. 5, 2014, pp. 549-554. https://doi.org/10.13067/JKIECS.201.9.5.549
  17. S. Hwang, "Channel estimation based on LMS algorithm for MIMO-OFDM system," J. of the Korea Institute of Electronic Communication Sciences, vol. 7, no. 6, 2012, pp. 1455-1461. https://doi.org/10.13067/JKIECS.2012.7.6.1455
  18. 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