基于拉普拉斯塔型变换的Contourlet变换频谱混叠特性分析

针对Contourlet变换存在频谱混叠的问题,立足于拉普拉斯(Laplace)塔型变换的分析研究,指出了Contourlet变换频谱混叠的根本原因在于Laplace塔型变换中两个低通滤波器不满足Nyquist抽样定律,致使阻带截全频率大于π/2,导致Contourlet变换的频谱混叠.基此.设计了满足Nyquist抽样定律的低通滤波器,提出了一种新型的Contourlet变换,即抗混叠Contourlet变换.抗混叠Contourlet变换有效地抑制了频谱混叠,基函数的空频局域件均明显优于Contourlet.通过对Barbara图像的硬阈值去噪实验研究结果表明,抗混叠Contourlet变换去噪在峰值信噪比(PSNR)上高出Contouet变换2.3 dB(噪声均方差为30),去噪效果好,同时还有效抑制了Contoulet变换去噪后的"划痕"现象,图像的视觉效果更佳.

Analysis of Frequency Aliasing of Contourlet Transform Based on Laplace Pyramidal Transform

A major drawback of the original contourlet transform is frequency aliasing, i.e., its basis images are not localized in the frequency domain. We analyze the cause of this problem from the aspect of Laplace pyramidal (LP) transform to make sure that the aliasing is caused by the reason that the two lowpass filters of LP transform do not satisfy with Nyquist-Shannon sampling theorem and its stopband frequency is more than π/2. Based on this reason, we design a new low-pass filter with stopband frequency smaller than π/2 and propose an anti-aliasing contourlet transform. The anti-aliasing contourlet is superior to contourlet transform in the respects of the regularity and localization of basis function, and depresses the frequency aliasing efficiently. Numerical experiments on peppers image denoising show that the proposed anti-aliasing contourlet transform can significantly outperform the original transform both in terms of peak signal-noise-ratio(PSNR) by 2.3 dB with noise root-mean-square of 30 and in visual quality. It also depresses the scratch phenomenon after anti-aliasing contourlet transform denosing.