抗混叠Curvelet变换非高斯双变量模型图像降噪

Image denoising using non-Gaussian bivariate model based on non-aliasing Curvelet transform

提出了一种基于非高斯双变量模型复数Curvelet变换的图像降噪新方法。采用具有近似移不变性的复数小波变换代替原Curvelet变换中的小波变换,并用改进的Radon变换避免了原Radon变换中一维傅里叶反变换在频域中采样不足的缺陷,从而保证了新的复数Curvelet变换具有抗混叠性能。充分利用信号系数层间相关性强而噪声系数层间相关性弱的特点,采用非高斯双变量对复数Curvelet变换域系数进行建模,并通过BayesianMAP估计器对信号系数进行估计,从而实现降噪目的。实验结果表明,本文去噪法得到的峰值信噪比(PSNR)分别比传统Curvelet去噪法和Curve-let域HMT去噪法平均提高2.9dB和1.5dB,且能避免重构图像中出现"划痕"和"嵌入污点",在有效去噪的同时,可较好地保护图像边缘和细节。

A new image denoising method using a non-Gaussian bivariate model in a Complex Curvelet Transform（CCT） domain is presented. For avoiding the shift-variance and under-sampling during the 1D inverse Fourier transform in the traditional Curvelet transform ,a new Curvelet transform, Complex Curvelet Transform（CCT）, is proposed by adopting the complex wavelet transform and reformative Radon transform to replace the traditional wavelet transform and the old Radon transform respectively,which provides a non-aliasing property for the proposed method. Because the inter-scale correlation of a signal coefficient is stronger than those of noise coefficients, the non-Gaussian bivariate model is used for capturing inter-scale correlation of the signal coefficient and for obtaining the denoised coefficient from the noisy image decomposition by a Bayesian MAP estimator. Experimental results show that the Peak Signel Noise Rotio（PSNR） of the proposed algorithm is averagely higher about 2.9 dB and 1.5 dB than those of the traditional Curvelet transform denoising method and Curvelet domain HMT denoising method respectively at all noise levels. The proposed method avoids ＂scratching＂ and ＂embedded blemishes＂ phenomena in the reconstructed image,and achieves an excellent balance between suppressing noises effectively and preserving image details and edges as many as possible.