Application Research Of Directionlet Transform In Image Denoising

Contour and directional information are intrinsic geometrical features of images. Standard two-dimensional wavelet transform is not the best tool for image processing, because it can not detect the contour information effectively, and only can obtain limited directional information of images. Directionlet transform is an anisotropic transform based on discrete integer lattice. It not only can capture the contour and edge of images efficiently, but also can acquire directional information along any two rational slopes. Directionlet transform has improved the deficiencies of standard wavelets; meanwhile it retains the separable filtering design and simplicity of computations.In this thesis, we thoroughly study the theory of directionlet transform, and investigate its application in image denoising. These are embodied through the following aspects:(1) The theory, implementation and shortcomings in image processing of standard two-dimensional wavelet transform are discussed. The theory and implementation of directionlet transform and nonsubsampled directionlet transform are particularly studied.(2) For image de-noising in transform domain, nonsubsampled directionlets is combined with Gaussian scale mixtures. According to practical experiences, Haar filter-bank is chosen which has excellent results in nonsubsampled condition; and it is compared with other wavelets.(3) The SAR image de-speckling is investigated based on directionlet transform; and, the speckle-suppression algorithm, combining nonsubsampled directionlet transform and Bayesian Maximum a Posteriori estimation, is proposed and achieved great speckle reduction.All the algorithms referred hereinbefore are compared with standard wavelet transform. The experimental results show that directionlet transform is satisfying for image de-noising and is a potential tool for image processing.