基于非下采样双树复小波域的双变量模型去噪算法  

Denoising Algorithm by Nonsubsampled Dual-tree Complex Wavelet Domain Bivariate Model

作　　者：殷明[1] 白瑞峰[1] 邢燕[1] 庞纪勇 魏远远[1] 

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《光子学报》2014年第10期131-137,共7页Acta Photonica Sinica

基　　金：安徽省自然科学基金项目(No.1308085MA09);安徽省教育厅基金项目(No.2013AJZR0039);校博士专项科研基金(No.2012HGBZ0653)资助

摘　　要：提出一种基于非下采样双树复小波域的图像去噪算法.首先分析非下采样双树复小波变换同一方向实部与虚部小波系数之间的相关性,通过实例及统计规律得到其联合概率分布近似服从于椭圆边界的单峰各向异性二维非高斯分布.然后把双变量统计模型引入到非下采样双树复小波变换实部和虚部小波系数中,将实部与虚部小波系数的联合概率分布作为双变量先验模型,得到了非下采样双树复小波变换自适应各向异性双变量去噪模型.该模型可以很好地体现实部与虚部小波系数之间的相关性.运用最大后验概率来估计从含噪图像的小波系数恢复原图像的系数,达到去噪目的.最后根据该模型得到了一种具有闭式解的去噪算法.实验表明:该算法比经典算法提高了一定的峰值信噪比,且有良好的视觉效果,较好地保持了图像中的纹理特征.A novel image denoising algorithm based on undecimated dual-tree complex wavelet transform domain was proposed.Firstly,the dependency among the real and imaginary parts of undecimated dualtree complex wavelet coefficients in the same direction was analyzed.According to the dependency characterization and empirical joint distribution of the original clean images,an elliptically contoured and anisoropic bivariate non-Gaussian statistical model was established to fit the empirical joint distribution of real and imaginary parts.Then the joint distribution as a prior model was modeled with an adaptive and anisoropic non-Gaussian bivariate statistical model as well as reflects the dependencies among coefficients.It finally uses a maximum posteriori probability from noise image to estimate the original image wavelet coefficients,so as to achieve the purpose of denoising.A denoising rule with the simple closed-form solution was derived from the model.The experimental results demonstrate that the proposed method can obtain better performances than other existing outstanding denoising algorithms in terms of peak signalto-noise ratio and achieve a better visual quality.It also offers a better recovery of texture information compared to others.

关 键 词：非下采样双树复小波变换 图像去噪 非高斯分布 双变量模型 最大后验概率 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]