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The Estimation of Radial Exponential Random Vectors in Additive White Gaussian Noise

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DOI: 10.4236/wsn.2009.14035    3,767 Downloads   7,316 Views   Citations

ABSTRACT

Image signals are always disturbed by noise during their transmission, such as in mobile or network communication. The received image quality is significantly influenced by noise. Thus, image signal denoising is an indispensable step during image processing. As we all know, most commonly used methods of image denoising is Bayesian wavelet transform estimators. The Performance of various estimators, such as maximum a posteriori (MAP), or minimum mean square error (MMSE) is strongly dependent on correctness of the proposed model for original data distribution. Therefore, the selection of a proper model for distribution of wavelet coefficients is important in wavelet-based image denoising. This paper presents a new image denoising algorithm based on the modeling of wavelet coefficients in each subband with multivariate Radial Exponential probability density function (PDF) with local variances. Generally these multivariate extensions do not result in a closed form expression, and the solution requires numerical solutions. However, we drive a closed form MMSE shrinkage functions for a Radial Exponential random vectors in additive white Gaussian noise (AWGN). The estimator is motivated and tested on the problem of wavelet-based image denoising. In the last, proposed, the same idea is applied to the dual-tree complex wavelet transform (DT-CWT), This Transform is an over-complete wavelet transform.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

P. KITTISUWAN, S. MARUKATAT and W. ASDORNWISED, "The Estimation of Radial Exponential Random Vectors in Additive White Gaussian Noise," Wireless Sensor Network, Vol. 1 No. 4, 2009, pp. 284-292. doi: 10.4236/wsn.2009.14035.

References

[1] Y. Zhou, S. Lai, L. Liu, and P. Lv, “An improved approach to threshold function de-noising of mobile image in CL2 multi-wavelet transform domain,” IEEE Signal Processing 2000.
[2] L. Sendur and I. W. Selesnick, “Bivariate shrinkage func-tions for wavelet-based denoising exploiting interscale de-pendency,” IEEE Transaction Signal Processing, Vol. 50, No. 11, pp. 2744–2756, November 2002.
[3] I. W. Selesnick “Estimation of laplace random vectors in adap-tive white Gaussian noise,” IEEE Transactions on Signal Proc-essing, Vol. 56, No. 8, pp. 3482–3496. August 2008.
[4] J. Portilla, V. Strela, M. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussian in the wavelet domain,” IEEE Transaction Image Processing, Vol. 12, No. 11, pp. 1338–1351, November 2003.
[5] N. G. Kingsbury, “Image processing with complex wavelets,” Phil. Transaction London A, September 1999.
[6] N. G. Kingsbury, “Complex wavelets for shift invariant analy-sis and filtering of signals,” Applied Computation, Harmon, pp. 243–253., May 2001.
[7] S. M. M. Rahman, M. O. Ahmad, and M. N. S. Swamy, “Bayesian wavelet-based image denoising using the Gauss-Hermite expansion,” IEEE Transaction Image Process-ing, Vol. 17, No. 10, pp 1755–1771, October 2008.
[8] H. Rabbani, M. Vafadust, G. Saeed and I. W. Selesnick. “Im-age denoising employing a bivariate Cauchy distribution with local variance in complex wavelet domain,” IEEE Signal Proc-essing, Vol. 9, pp. 203–208, 2006.
[9] M. A. Chaudhry and S. M. Zubair, “Generalized incomplete gamma functions with application,” Journal of Computer Ap-plied Mathematic, Vol. 55, No. 1, pp. 99– 124, 1994.
[10] M. A. Chaudhry and S. M. Zubair, “On a class of incomplete gamma functions with applications,” New York: Chapman& Hall, 2001.
[11] D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika, Vol. 81, No. 3, pp. 425–455, 1994.
[12] S. C. Choi and R. Wette, “Maximum likelihood estimation of the parameters of the gamma distribution and their bias,” Technometric, Vol. 11, No. 4, pp. 683-690, 1969.
[13] M. K. Mihcak, I. Kozintsev, K. Ramchandran and P. Moulin, “Low-complexity image denoising based on statistical model-ing of wavelet coefficients.” IEEE Signal Processing Letters, Vol. 6, No. 12, pp. 300-303, December 1999.
[14] R. W. D. Nickalls, “A new approach to solving the cubic: Car-dan's solution revealed,” The Mathematical Gazette, Vol. 77, pp. 354–359, 1993.

  
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