中文摘要：

摘要：图像去噪一直是图像处理的经典问题之一。四元数小波变换是一种新的多尺度分析图像处理工具，图像通过四元数小波变换后的小波系数尺度间具有一定的相关性，而广义高斯分布不能体现这个特性。本文首先采用非高斯二元分布的贝叶斯统计模型来模拟四元数小波系数的统计分布，然后运用最大后验概率估计从带噪声图中的小波系数估计原图的小波系数，从而达到去除噪声的目的。实验表明；该方法不仅可以达到明显的去除噪声的效果，而且在峰值信噪比上也要优于目前的许多算法。

英文摘要：

Image denoising is always one of the classical problems of the image processing. Quaternion wavelet transform is a new kind of image processing tool for multi-scale analysis. The image via quaternion wavelet transform, its coefficients in intra-scale have certain correlations, while applying generalized Gaussian distribution cannot reflect the characteristics. First, the non-Gaussian bivariate distribution of Bayesian statistical model is used to simulate the statistical distribution of quaternion wavelet coefficients. Then it uses a maximum posteriori probability from noise image to esti- mate the original image wavelet coefficients, so as to achieve the purpose of denoising. The experiments show that this method can not only get conspicuously denoising result, but also in peak value signal-to-noise ratio be better than many algorithms.