Soft Thresholding Method Using Gabor Cosine and Sine Transform for Image Denoising

영상 잡음제거를 위한 게이버 코사인과 사인 변환의 소프트 문턱 방법

  • Published : 2010.01.30

Abstract

Noise removal methods for noisy images have been studied a lot in the domain of spatial and transform filtering. Low pass filtering was initially applied in the spatial domain. Recently, discrete wavelet transform has widely used for image denoising as well as image compression due to an excellent energy compaction and a property of multiresolution. In this paper, Gabor cosine and sine transform which is considered as human visual filter is applied to image denoising areas using soft thresholding technique. GCST is compared with excellent wavelet transform which uses existing soft thresholding methods from PSNR point of view. Resultant images removed noises are also visually compared. Experimental results with adding four different standard deviation levels of Gaussian distributed noises to real images show that the proposed transform has better PSNR performance of a maximum of 1.18 dB and visible perception than wavelet transform.

영상에 존재하는 잡음을 제거하는 방법은 공간영역과 변환영역에서 많은 연구가 되어 왔다. 초기에는 공간영역에서 저역통과필터를 많이 사용하였으나, 최근에는 변환영역에서 이산 웨이브릿 변환이 탁월한 에너지 집중도와 다분해능 성질에 기인하여 영상압축 뿐만 아니라 잡음제거에도 많이 사용되고 있다. 본 논문은 인간시각필터로 고려되는 Gabor 코사인과 사인 함수를 이용한 변환을 소프트 문턱치 기법으로 영상 잡음제거 응용에 적용하고자 한다. 기존 소프트 문턱치 기법을 이용하는 우수한 웨이브릿 변환과 PSNR 성능을 비교하고, 잡음 제거된 결과 영상을 시각적으로도 비교한다. 4가지 Gaussian 분포 잡음을 첨가한 여러 실제 영상의 실험으로부터 제안한 변환이 PSNR 성능에서 최대 1.18dB 우수하고, 시각적 인지에서도 분명한 차이를 보였다.

Keywords

References

  1. M. C. Motwani, M. C. Gadiya, and R. C. Motwani, "Survey of Image Denoising Techniques," Proceedings of GSPx 2004, Santa Clara Convention Center, Santa Clara, pp. 21-27, Sept. 27-30, 2004.
  2. P. Gruber, F. J. Theis, A. M. Tome, and E. W. Lang, "Automatic Denoising Using Local Independent Component Analysis," Fourth Int'l ICSC Symp. on Eng. in Intelligent Systems 2004, Madeira, Portugal, pp. 127-130, Feb. 29-Mar. 2, 2004.
  3. D. L. Donoho and I. M. Johnstone, "Ideal Spatial Adaption via Wavelet Shrinkage," Biometrika, vol. 81, pp. 425-455, Sept. 1994, https://doi.org/10.1093/biomet/81.3.425
  4. D. L. Donoho, "De-noising by Soft-Thresholding," IEEE Trans. on Information Theory, vol. 41, no. 3, pp. 613-627, May 1995. https://doi.org/10.1109/18.382009
  5. D. L. Donoho and I. M. Johnstone, "Ideal Spatial Adaption via Wavelet Shrinkage," Biometrika, vol. 81, pp. 425-455, Sept. 1994. https://doi.org/10.1093/biomet/81.3.425
  6. S. G. Chang, B. Yu, and M. Vattereli, "Adaptive Wavelet Thresholding for Image Denoising and Compression," IEEE Trans. on Image Processing, vol. 9, pp. 1532-1546, Sept. 2000. https://doi.org/10.1109/83.862633
  7. L. Kaur, S. Gupta, and R. C. Chauhan, "Image Denoising Using Wavelet Thresholding," Indian Conf. on CVGIP, Space Applications Centre, Ahmedabad, India, pp. 77-80, Dec. 16-18, 2002.
  8. P, Moulin and J. Liu, "Analysis of Multiresolution Image Denoising Schemes Using Generalized Gaussian and Complexity Priors," IEEE Trans. on Information Theory, vol. 45, no. 3, pp. 909-919, Apr. 1999. https://doi.org/10.1109/18.761332
  9. J. Romberg, H. Choi, and R. G. Baraniuk, "Bayesian Wavelet Domain Image Modeling Using Hidden Markov Models," IEEE Trans. on Image Processing, vol. 10, pp. 1056-1068, July 2001. https://doi.org/10.1109/83.931100
  10. D. L. Donoho and I. M. Johnstone, "Adapting to Unknown Smoothness via Wavelet Shrinkage," Journal of the American Statistical Assoc., vol. 90, no. 432, pp. 1200-1224, Dec. 1995. https://doi.org/10.2307/2291512
  11. Y. H. Lee and S. B. Rhee, "Wavelet-based Image Denoising with Optimal Filter," International Journal of Information Processing Systems, vol. 1, no. 1, pp. 32-35, 2005. https://doi.org/10.3745/JIPS.2005.1.1.032
  12. L. Sendur and I. W. Selesnick, "Bivariate Shrinkage Functions for Wavelet-Based Denoising Exploiting Interscale Dependency," IEEE Trans. on Signal Processing, vol. 50, no. 11, pp. 2744-2756, Nov. 2002. https://doi.org/10.1109/TSP.2002.804091
  13. F. Luisier and T. Blu, "SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding," IEEE Trans. on Image Processing, vol. 17, no. 4, pp. 482-492, Apr. 2008. https://doi.org/10.1109/TIP.2008.919370
  14. 이적식, "Gabor 코사인과 사인 변환," 전자공학회논문지, 제39권 SP편 제4호, pp. 408-417, 2002년 7월.
  15. 이적식, "GCST를 이용한 인간시각필터의 영상 잡음제거," 한국신호처리.시스템학회 논문지, 제9권 4호, pp. 253-260, 2008년 10월.
  16. J. A. Bloom and T. R. Reed, "A Gaussian derivative-based transform," IEEE Trans. on Image Processing, vol. 5, no. 3, pp. 551-553, Mar. 1996. https://doi.org/10.1109/83.491330
  17. L. E. Franks, Signal Theory, Dowden & Culver, pp. 35-38, 1981.
  18. C. S. Burrus, R. A. Gopinah, and H. Guo, Introduction to Wavelets and Wavelet Transforms, New Jersey, Prentice Hall, pp. 110-120, 1998.