A Bivariate Shrinkage Function for Complex Dual Tree Dwt Based Image Denoising

For many natural signals, the wavelet transform is a more effective tool than the Fourier transform. The wavelet transform provides a multi resolution representation using a set of analyzing functions that are dilations and translations of a few functions. The wavelet transform lacks the shift-invariance property, and in multiple dimensions it does a poor job of distinguishing orientations, which is important in image processing. For these reasons, to obtain some applications improvements, the Separable DWT is replaced by Complex dual tree DWT. In this paper, we propose a new simple non Gaussian bivariate probability distribution function to model statistics of wavelet coefficients of 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. The new shrinkage function, which depends on both the coefficient and its parent, yields improved results for complex wavelet-based image denoising. Key-Words: Complex DWT, Denoising, Bivariate Shrinkage Function