复张量场扩散方程及其在PolSAR图像去噪中的应用

张量图像如极化合成孔径雷达(PolSAR)图像,它的每一个像素点都是一个3 阶的正定对称矩阵。对于张量图像的噪声抑制,目前普遍的做法是将它们看作多通道标量图像进行处理,但是,这样可能会破坏矩阵的正定性,从而造成信息的损失。本文主要研究基于扩散方程的张量图像的噪声抑制问题,将现有的基于扩散方程的实张量场去噪模型推广到复张量场,并给出了其数值迭代格式。模拟图像和PolSAR图像上的实验充分验证了本文算法的有效性。与现有算法相比,本文算法具有更好的去噪能力和边缘保持能力。

Anisotropic Diffusion on Complex Tensor Fields for PolSAR Image Filtering

Each pixel of a tensor image is usually characterized by a 3-order positive definite matrix. Currently, existing methods of denoising tensor images usually regard the data as multi-channel images, which is likely to destroy the structure of positive definite matrices of the image and some information will be missed possibly. This paper addresses the problem of denoising complex tensor images. More precisely, we extend the anisotropic diffusion model, also known as P-M model, from scalar or vector images to complex tensor ones. The proposed method can be applied to remove speckle noises in PolSAR images. In contrast with existing denosing algorithms, our method is better at suppressing the effects of speckles while preserving edges.