复数Curvelet变换域复数高斯尺度混合图像降噪

Image Denoising Using Complex Gaussian Scale Mixtures in Complex Curvelet Transform Domain

提出了一种基于复数Curvelet变换域复数高斯尺度混合(CGSM)模型的图像去噪方法.指出Curvelet变换重构图像存在"划痕"和"嵌入污点"的主要原因是Curvelet变换域存在频谱混叠,为此,采用复数小波变换和改进的Radon变换分别代替原Curvelet变换中的实小波变换和Radon变换.构造了具有抗混叠性能的复数Curvelet变换.本文同时把高斯尺度混合(GSM)模型扩展到复小波域,形成对复小波系数的幅值和相位信息具有有效捕捉能力的复数GSM模型,并在复数Curvelet变换域,采用贝叶斯最小平方(BLS)估计器对CGSM模型下含噪复系数进行有效估计,从而实现降噪.实验结果表明,无论是用PSNR指标评估,还是在视觉效果上,本文方法的去噪性能均好于传统Curvelet去噪、Curvelet域HMT去噪和小波域BLS-GSM去噪.本文方法在有效去噪的同时,具有很好的图像边缘和细节保护能力.

An image denoising method using complex Gaussian scale mixtures （CGSMs） model in complex Curvelet transform （CCT） domain is presented. The reason of ＂scratches＂ and ＂embedded stain＂ in the Curvelet transform reconstruction image is pointed out that aliasings exist in Curvelet transform domain. So, a new non-aliasing Curvelet transform, namely CCT, is proposed by using complex wavelet transform and improved Radon transform to replace real wavelet transform and old Radon transform in the original Curvelet transform respectively. The Gaussian scale mixtures （GSMs） model is extended into complex wavelet domain and becomes a CGSM model which can capture both magnitude and phase information of the complex wavelet coefficients availably. In the CCT domain, the noisy coefficients in the CGSM model can be estimated effectively by using Bayesian least squares （BLS） estimator, so noise reduction can be achieved. Experimental results show that, whether judged by PSNR index or in visual effect, the proposed scheme outperforms the traditional Curvelet transform denoising, Curvelet domain HMT denoising and wavelet domain BLS-GSM denoising. Plus, it has a good ability to preserve image details and edges while suppressing noise effectively.