一种循环平移的Contourlet变换去噪新方法

与小波变换相比，Contourlet变换等多尺度几何分析方法，可以更好地逼近含线奇异的高维函数。针对Contourlet变换缺乏平移不变性的缺陷，提出了一种基于Contourlet变换以及循环平移的图像去噪方法，即MCT方法。由于阈值去噪会在重构的图像中产生虚假成分（视觉魇像），尤其是在奇异点附近交替出现较大的上下幅值振动。而循环平移的目的就是在给定范围内寻求最佳平移量（或平均平移量），通过改变图像的排列次序，从而改变奇异点在整个图像中的位置来达到减小或消除振荡幅度，进而改善由于伪Gibbs现象所导致的蚊状噪声。实验表明，与抽样小波去噪相比，该方法明显可以更好地保持图像边缘；同时也一定程度上改进了传统Contourlet变换去嗓方法所带来的视觉魇像的缺点，较好的保留了图像的细节部分，且峰值信噪比（PSNR）也较高。

A Novel De-noising Method in Contourlet Domain with Cycle Spinning

The Muhiscale Geometrical Analysis including Contourlet transform is one kind of optimal representation of line singularity of high dimensional function. We propose a new method for image denoising based on the contourlet transform. Due to the lack of translation - invariance of contourlet transform, we employ a cycle spinning approach, i. e. , MCT algorithm. The denoising method via thresholding will introduce artifacts in reconstruction image, especially in the neighborhood of edges and textures. The proposed approach tries to change the relative position of singularity point/line in an image. The aim of cycle translation is to find the optimal/average spinning within a specific range and to smooth the artifacts due to the Gibbs - like phenomenon. The experimental results show that this method outperforms the translation variant contourlet transform and decimates wavelet transform both visually and in terms of PSNR.