中文摘要：

基于传统Contourlet变换及已有相关改进方法存在频谱混叠或移变性的缺点，其处理后的图像会出现伪吉布斯现象，严重影响了图像的质量，因此提出一种既抗混叠又有平移不变性的Contourlet变换新方法来克服这两个缺点．新方法是一种结合了抗混叠塔式滤波器组和非下采样方向滤波器组的方法．通过比较新方法和相关Contourlet变换方法的非线性逼近性能和降噪效果，表明新方法更能稀疏地表示图像，且在降噪性能上有较大的提高：它不仅有效地克服了因频谱混叠和移变性所带来的“刮痕”现象，而且能更好地保护图像的边缘和纹理细节信息．

英文摘要：

The traditional contourlet transform and its improved methods have been identified with some drawbacks such as spectral aliasing or shift-invariance. The processed image by these methods will appear pseudo-Gibbs phenomena, which pose adverse impacts on the quality of the image. In this paper, a modified method is proposed to overcome these two major drawbacks, which adopts contourlet transform with anti-aliasing and shifl-invariance. The new method is constructed as a combination of the anti-aliasing pyramid filter bank and the nonsubsampled directional filter bank. Through comparing the nonlinear approximation performance and the denoising effect with the related contourlet transform methods, it is found that the proposed method has better sparse performance and greatly improved denoising effect. In addition, it efficiently overcomes the ＂scratches＂ phenomena caused by spectrum aliasing and shift-invariance, and has better ability to protect image＇s edges and texture details.