Performance Improvement in the Bivariate Models by using Modified Marginal Variance of Noisy Observations for Image-Denoising Applications

Authors: R. Senthilkumar

Abstract:

Most simple nonlinear thresholding rules for wavelet- based denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependencies. This paper attempts to give a recipe for selecting one of the popular image-denoising algorithms based on VisuShrink, SureShrink, OracleShrink, BayesShrink and BiShrink and also this paper compares different Bivariate models used for image denoising applications. The first part of the paper compares different Shrinkage functions used for image-denoising. The second part of the paper compares different bivariate models and the third part of this paper uses the Bivariate model with modified marginal variance which is based on Laplacian assumption. This paper gives an experimental comparison on six 512x512 commonly used images, Lenna, Barbara, Goldhill, Clown, Boat and Stonehenge. The following noise powers 25dB,26dB, 27dB, 28dB and 29dB are added to the six standard images and the corresponding Peak Signal to Noise Ratio (PSNR) values are calculated for each noise level.

Keywords: BiShrink, Image-Denoising, PSNR, Shrinkage function

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1063062

References:

[1] D.L. Donoho and I.M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage", Biometrika, vol. 81, pp 425-455, 1994.
[2] D.L. Donoho, "De-noising by soft-thresholding", IEEE Trans. Inform. Theory, vol.41, pp 613-627, May 1995.
[3] 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, December 1995.
[4] C.M. Stein, "Estimation of the mean of a multivariate normal distribution", Ann. Statist., vol.9, no.6, pp 1135-1151, 1981.
[5] S.G. Chang, Bin Yu and M. Vetterli, "Adaptive wavelet thresholding for image denoising and compression", IEEE Trans. Image processing, vol. 9, pp 1532-1546, September 2000.
[6] L. Sendur and I. W. Selesnick, "A bivariate shrinkage function for wavelet based denoising", IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), pp 1261-1264, 2002.
[7] L. Sendur and I. W. Selesnick, "Bivariate shrinkage with local variance estimation", IEEE Signal Processing Letters, vol.9, no.12, pp 438-440, December 2002.
[8] 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, November 2002.
[9] L. Sendur and I.W. Selesnick, "Subband Adaptive Image Denoising Via Bivaraite Shrinkage", IEEE Int. Conf. Image Processing (ICIP), pp 577- 580, 2002.