An Improved Wavelet-based Contourlet Transform And Research On Its Application To Image Denoising

Wavelets have the advantages of multiscale and multiresolution analysis, which are widely used in signal analysis and processing. The wavelet transform is optimal in capturing the one-dimensional singularities. As a result of a separable extension from 1-D bases, wavelets can not make the most of geometrical characters of the images. While the edge, contour or texture contains much information in which we are interested, wavelets are not the optimal representations in higher dimensions. Because of the limitation, a theory named Multiscale Geometry Analysis (MGA) was proposed. This theory is developing in theories and applications.The Directional filter banks (DFB) can decompose the image into direction subbands, which have a great development in MGA. Recently, some geometrical image transforms based on the DFB have been introduced. In this paper we focus on the wavelet-based contourlet transform (WBCT). It is sensitive to the texture information of the image, and has been widely used in image processing. However, directional filter banks applied to the WBCT are lack of translation invariance, which could cause visual artifacts by setting some transform coefficients to zero for denoising. A new multiresolution nonsubsampled geometrical image transform is proposed to solve this problem, wavelets and nonsubsampled directional filter banks (WNSDFB). It is implemented by the wavelet transform in conjunction with nonsubsampled directional filter banks (NSDFB). Taking advantage of the wavelet transform that has efficient nonlinear approximation property, the important features of directionality and translation invariance are added by applying NSDFB to all subbands of the wavelet. The artifacts usually introduced by DFB are eliminated. The proposed WNSDFB transform provides visual and PSNR improvements over the wavelet and WBCT transforms. Finally, its application to SAR image denoising is discussed.