中文摘要：

图像的去噪和压缩一直是图像处理的经典问题,传统的方法中很难将二者同时兼顾。四元数小波变换是实小波、四元数理论及二维希尔伯特变换相结合的产物,是一种新的多尺度分析图像处理工具。图像经四元数小波变换后,其小波系数不仅在尺度内具有相关性,而且在尺度间也具有一定的相关性。文中提出一种混合统计模型,该模型包括尺度间的二元非高斯分布模型和尺度内的广义高斯分布模型,然后运用最小均方误差（MMSE）估计从噪声图中的小波系数恢复原图的系数,从而达到去除图像的噪声的目的。仿真实验表明,论文方法不仅可以获得信噪比上的提高、视觉上达到明显的去噪效果,而且取得了较高的压缩比。

英文摘要：

Image denoising and compression has been the classic image processing problem,and traditional methods are difficult to reach both requirements.Quaternion wavelet transform is the product of the combination of real wavelet,complex wavelet,quaternion theory and 2D-hilbert transform,and it is a new kind of multiresolution analysis of image processing tools.After quaternion wavelet transform,Image wavelet coefficients have certain intrascale and interscale correlation.This paper presents a mixed statistical model,which includes interscale bivariate non-Gaussian distribution and intrascale generalized Gaussian distribution.The minimum mean square error（MMSE） is used to estimate original image coefficients from wavelet coefficients with noise,so as to achieve the purpose of denoising.The experiment results show that this method can not only get signal-to-noise ratio enhancement and better visual quality,but also achieve high compression ratio.