极化合成孔径雷达（SAR）图像受相干斑噪声的影响，难以很好地保持结构特性，针对这个问题提出了一种采用3维块匹配小波变换的非局部均值滤波算法NL-3DWT（Nonlocal Filter based on 3-D Patch Matching Wavelet Transform）。该算法使用块匹配的3维非抽样小波变换对极化总功率图进行预滤波，在此基础上使用边界对齐窗提取结构相似像素，同时使用Sigma范围选择极化SAR数据的散射相似像素，共同构成相似像素集合；构建结构保持权重函数增大图像结构信息在块相似性度量时的权重，最终实现极化SAR图像结构保持的相干斑抑制。该算法增强了图像结构特征的表达，提高了结构相似像素选择的准确性，机载极化SAR数据实验结果表明，NL-3DWT算法能够在抑制相干斑噪声的同时，更有效地保持极化SAR图像的结构特性和极化散射特性。

The Polarimetric Synthetic Aperture Radar (PolSAR) system has unique advantages in observing the Earth's surface at different times and weather conditions. However, PolSAR data restricted to an inherent imaging mechanism are corrupted by speckle noise. The presence of speckle increases the difficulty of image understanding and decreases the accuracy of subsequent image segmentation and classification. Thus, the research on the algorithms of PolSAR image speckle reduction has important theoretical significance and practical value.
A non-local filter based on the three dimensional patch matching wavelet transform (NL-3DWT) was proposed to solve the problem of preserving the structural characteristics in the despeckling of PolSAR images. First, the algorithm combined an undecimated wavelet transform with the three dimensional patch group that consists of similar patches and then applied the combination to the span (or total power) image. Local linear minimum mean square error estimation was subsequently utilized to shrink the coefficients in the wavelet domain before the inverse three dimensional wavelet transform to obtain the updated span image. Second, the edge-aligned windows selected the structural similar pixels in the updated span image. The Sigma range selected the scattering similar pixels by employing the original PolSAR data. These similar pixels were adopted to construct a pixel set to participate in the final non-local means filtering. Third, the structural similarity index based on the similar pixels set was introduced to calculate the structural preserving weight function, which was utilized in the non-local means filtering with the original PolSAR data.
Two sets of PolSAR data detected by the airborne AIRSAR system were adopted to verify the effectiveness of the proposed algorithm in terms of three aspects:speckle reduction, structural features preservation, and polarimetric features preservation. Considering its relevance to this study, the NL-3DWT algorithm was compared with the classical refined PolSAR filtering method of Lee and two types of the latest PolSAR nonlocal filter methods (i.e., NL-Pretest and NL-HPP). The three methods all employed the parameters derived from their respective studies to yield convincing results.
The resulting images or evaluation indexes, such as Equivalent Number of Looks (ENL), Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE), and Edge Preservation Index (EPI), show that the NL-3DWT method effectively lowered the speckle and retained edge details in the speckle reduction and structural features preservation processes. In contrast, the Refined Lee still had residual speckle. Furthermore, the NL-Pretest resulted in over-filtering that appeared as false targets, although it suppressed the speckle noise. The NL-3DWT algorithm also more effectively preserved the polarimetric scattering mechanisms than the NL-HPP in terms of the H-Alpha scatter plots in the polarimetric features preservation.
The proposed method can increase the accuracy of structurally similar pixel selection, enhance the expression of image structure features, and improve the weight of image structural information in the similarity measurement between patches. Test results demonstrate that the NL-3DWT algorithm effectively lower the speckle and retains the structural characteristics and polarimetric scattering characteristics in PolSAR images. However, the algorithm complexity causes difficulties in the real-time processing of PolSAR images. Hence, studying the fast algorithm must be considered.