Spatially adaptive image denoising using inter-scale dependence in directionlet domain

The performance of image processing algorithms can be significantly improved by the application of multi-resolution image representation with directional features. Directionlet transform (DT) is one such representation which has gained popularity over the past few years as an anisotropic, perfect reconstruction and critically sampled basis function with directional vanishing moments along any two directions. In this study, the authors propose a spatially adaptive image denoising scheme for Gaussian noise based on DT by considering the dependences of the directionlet coefficients across different scales. The image is first decomposed using DT and the coefficients so obtained are modelled using a bivariate heavy tailed `pdf´ with a local variance parameter to account for inter- and intra-scale dependencies of the coefficients. The DT is made adaptive to the local dominant directions in the image by identifying the dominant directions in the spatially segmented image through the computation of a parameter called `directional variance´. Bayesian `maximum a posteriori´ estimator is then used to compute the noise free coefficients from the bivariate models of the signal and noise. The denoised image is obtained from the transform coefficients, which were modified using the bivariate shrinkage function, using directional information and inverse DT. Experimental results show that the bivariate shrinkage in directionlet domain achieves better performance than that in wavelet domain, in terms of numerical and perceptual quality.