Bivariate Shrinkage Functions for Wavelet-based Image Denoising

Levent Sendur and Ivan Selesnick


We propose a new simple non-Gaussian bivariate probability distribution function to model the statistics of wavelet coefficients of natural images. The model captures the dependence between a wavelet coefficient and its parent. Using Bayesian estimation theory we derive from this model a simple non-linear shrinkage function for wavelet denoising, which generalizes the soft thresholding approach of Donoho and Johnstone. The new shrinkage function, which depends on both the coefficient and its parent, yields improved results for wavelet-based image denoising. (Extended abstract.)

Bivariate Shrinkage Functions for Wavelet-based Image Denoising. IEEE Transactions on Signal Processing, 50(11):2744-2756, November 2002.

Download the four page conference paper as a PDF file or as a zipped PDF file. In Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), Orlando, May 13-17, 2002.

An improved version of the denoising method uses a local estimate of the signal variance: Bivariate shrinkage with local variance estimation, IEEE Signal Processing Letters, 9(12):438-441, December 2002.

bivariate shrinkage function.