中文摘要：

为了反映合成孔径雷达图像中斑点噪声尖峰厚尾的统计特征，使用拖尾Rayleigh分布来描述斑点噪声，基于Gamma先验分布和斑点噪声的拖尾nayleigh分布，推导出了合成孔径雷达图像的最大后验概率滤波方程，并给出了它在特定特征参数时的解析形式。使用Mellin变换从观察图像估计拖尾nayleigh分布的未知参数，给出了在斑点噪声的拖尾Rayleigll分布下的最大后验概率降噪试验和量化指标，为了消除滑动窗大小和噪声强度对降噪结果的影响，给出了降噪能力随滑动窗大小和噪声方差的动态变化关系。结果表明，拖尾Rayleigh分布尖峰厚尾的特征符合斑点噪声的真实统计特性，因此与Rayleigh分布以及Kuan滤波相比，基于斑点噪声的拖尾nayleigh分布的最大后验概率滤波具有较强的降噪能力。

英文摘要：

In order to reflect the statistics of high peak and heavy tail, speckle in synthetic aperture radar images is modeled as heavy- tailed Rayleigh distribution. First, based on Gamma prior distribution and heavy-tailed Rayleigh distribution of speckle, the maximum a pesteriori filtering equation is proposed and its analytical form is provided in given characteristic parameter. Second, parameters of heavy-tailed Rayleigh distribution are estimated from the observed image using Mellin transformation. Last, maximum a pesteriori de-speckling experiments and their quantitative measures are given. In order to eliminate the influence of window size and noise intensity on de-speckling results, dynamic relations of the de-speckling capability to noise variance and window size are suggested respectively. Results demonstrate that the heavy-tailed Rayleigh distribution accords with the real statistics of speckle, so the maximum a pesteriori filter in heavy-tailed Rayleigh distribution of speckle has higher capability of noise reduction compared to the one in Rayleigh distribution of speckle and the Kuan filter.