Journal of the Institute of Electronics Engineers of Korea SP (대한전자공학회논문지SP)

The Institute of Electronics and Information Engineers (대한전자공학회)
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Bayesian Image Denoising with Mixed Prior Using Hypothesis-Testing Problem

가설-검증 문제를 이용한 혼합 프라이어를 가지는 베이지안 영상 잡음 제거

  • Eom Il-Kyu (Dept. of Electronics Engineering, Research Institute of Computer, Information and Communication) ;
  • Kim Yoo-Shin (Dept. of Electronics Engineering, Pusan National University)
  • 엄일규 (부산대학교 전자공학과, 컴퓨터및정보통신연구소) ;
  • 김유신 (부산대학교 전자공학과)
  • Published : 2006.05.01
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Abstract

In general, almost information is stored in only a few wavelet coefficients. This sparse characteristic of wavelet coefficient can be modeled by the mixture of Gaussian probability density function and point mass at zero, and denoising for this prior model is peformed by using Bayesian estimation. In this paper, we propose a method of parameter estimation for denoising using hypothesis-testing problem. Hypothesis-testing problem is applied to variance of wavelet coefficient, and $X^2$-test is used. Simulation results show our method outperforms about 0.3dB higher PSNR(peak signal-to-noise ratio) gains compared to the states-of-art denoising methods when using orthogonal wavelets.

일반적으로 웨이블릿 계수는 적은 수의 계수에 거의 대부분의 정보가 저장되어 있다. 이러한 웨이블릿 계수의 성긴 특성은 가우스 확률밀도 함수와 영점에서의 점 질량(point mass) 함수의 혼합으로 모델링될 수 있으며, 이 프라이어(prior) 모델에 대한 베이지안 추정법으로 잡음 제거를 수행한다. 본 논문에서는 가설-검증 기법을 이용하여 잡음 제거를 위한 파라미터를 추정하는 방법을 제안한다. 가설-검증은 관찰된 웨이블릿 계수의 분산에 적용되며, $X^2$-검증을 사용한다. 모의실험 결과를 통하여 본 논문의 방법이 직교 웨이블릿 변환을 사용한 최신의 잡음 제거 방법보다 대략 0.3dB 정도 우수한 PSNR(peak signal-to-noise ratio) 성능을 나타낸다.

Keywords

References

  1. D. L. Donoho and 1. M. Jonhstone, 'Adapting to unknown smoothness via wavelet shrinkage,' J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1200- 1224, 1995 https://doi.org/10.2307/2291512
  2. M. K. Mihcak, I. Kozintsev, K. Rarnchandran, and P. Moulin, 'Low-complexity image denoising based on statistical modeling of wavelet coefficients,' IEEE Signal Processing Letters, vol. 6, pp. 300-303, 1999 https://doi.org/10.1109/97.803428
  3. S. G. Chang, B. Yu, and M. Vetterli, 'Spatially adaptive wavelet thresholding with context modeling for image denoising,' IEEE Trans. Image Processing, vol.9, pp.1522-1531, 2000 https://doi.org/10.1109/83.862630
  4. M. K. Mihcak, I. Kozintsev, K. Rarnchandran, 'Spatially Adaptive statistical Modeling of Wavelet Image Coefficients and Its Application to Denosing,' Proc, IEEE Int. Conf. Acous., Speech and Signal Processing, vol.6, pp. 3253-3256, 1999 https://doi.org/10.1109/ICASSP.1999.757535
  5. J. Liu and P. Moulin, 'Image denoising based on scale-space mixture modeling of wavelet coefficients,' Proc. IEEE Int. Conf. on Image Processing, Kobe, Japan, 1999 https://doi.org/10.1109/ICIP.1999.821636
  6. J. K. Romberg, H. Choi, and R. G. Baraniuk, 'Bayesian tree-structured image modeling using wavelet-domain hidden Markov models,' IEEE. Trans. Image Processing, vol.10, no.7, pp. 1056-1068, 200l https://doi.org/10.1109/83.931100
  7. H. Choi, J. Romberg, R. Baraniuk, and N. Kingsbury, 'Hidden Markov Tree Modeling of Complex Wavelet Transforms,' Proc. IEEE Int. Conf. Acous., Speech and Signal Processing, Istanbul, Turkey, June, 2000 https://doi.org/10.1109/ICASSP.2000.861889
  8. L. Sendur and I. W. Selesnick, 'Bivariate shrinkage with local variance estimation,' IEEE Signal Processing Letters, vol.9, no.12, pp.438-441, 2002 https://doi.org/10.1109/LSP.2002.806054
  9. Z. Cai, T. H. Cheng, C. Lu, and K R. Subramanian, 'Efficient wavelet based image demising algorithm,' Electron. Lett., vol. 37, no.11, pp.683-685, 2001 https://doi.org/10.1049/el:20010466
  10. J. Pirtilla, V. Strela, M. Wainwright and E Simoncelli, 'Adaptive Wiener Denoising Using a Gaussian Scale Mixture Model,' Proc. IEEE Int. Conf. on Image Processing, 2001 https://doi.org/10.1109/ICIP.2001.958418
  11. J. C. Pesquet, H. Krim, D. Leporini and E. Hamman, 'Bayesian Approach to Best Basis selection,' IEEE Int. Conf. Acous., Speech and Signal Processing, pp. 2634-2637, 1996 https://doi.org/10.1109/ICASSP.1996.548005
  12. Hugh A. Chipman, Eric D. Kolaczyk, and Robert E. McCulloch, 'Adaptive Bayesian Wavelet Shrinkage,' Journal of the American Statistical Association, vol.92, pp.1413-1421, 1997 https://doi.org/10.2307/2965411
  13. B. Vidakovic, 'Wavelet Based Nonparametric Bayes Methods,' Lecture note in Statistics, vol.133, pp.133-155, 1998
  14. E. J. Dudewicz, and S. N. Mishra, Modern Mathematical Statistics, John Wiley & Sons, 1988
  15. E. H. Adelson, E. Simoncelli, and R. Hingorani, 'Orthogonal pyramid transforms for image coding,' Proc. SPIE, vol.845, pp.50-58, 1987