Image denoising based on adaptive spatial segmentation and multi-scale correlation in directionlet domain

Directionlet transform DT has become popular over the last few years as an efficient image representation tool due to its fine frequency tiling and directional vanishing moments along any two directions. A novel denoising algorithm based on DT is proposed here for images corrupted with Gaussian noise. The image is first spatially segmented based on the content directionality. Then an undecimated version of DT is applied to effectively capture the directional features and edge information of these segments. The DT coefficients so obtained are then modelled using a bivariate heavy tailed Gaussian distribution and the noise free coefficients are computed using MAP estimator. By employing bivariate probability distribution, the heavy-tail behaviour of natural images is accurately modelled and the interscale properties of DT coefficients are properly exploited. In addition, the local variance parameter of the model is estimated based on classification of DT coefficients within a particular scale using context modelling. Due to this the intrascale dependency of the directionlet coefficients is also well exploited in the enhancement process. The proposed algorithm is competitive with the existing algorithms with better results in terms of output peak signal-to-noise ratio while having comparable computational complexity. It exhibits good capability to preserve edges, contours and textures especially in images with abundant high frequency contents.