Deep learning is an effective end-to-end method for Polarimetric Synthetic Aperture Radar(PolSAR) image classification, but it lacks the guidance of related mathematical principle and is essentially a black-box model. In addition, existing deep models learn features in Euclidean space, where PolSAR complex matrix is commonly converted into a complex-valued vector as the network input, distorting matrix structure and channel relationship. However, the complex covariance matrix is Hermitian positive definite (HPD), and resides on a Riemannian manifold instead of a Euclidean one. Existing methods cannot measure the geometric distance of HPD matrices and easily cause some misclassifications due to inappropriate Euclidean measures. To address these issues, we propose a novel Riemannian Sparse Representation Learning Network (SRSR CNN) for PolSAR images. Firstly, a superpixel-based Riemannian Sparse Representation (SRSR) model is designed to learn the sparse features with Riemannian metric. Then, the optimization procedure of the SRSR model is inferred and further unfolded into an SRSRnet, which can automatically learn the sparse coefficients and dictionary atoms. Furthermore, to learn contextual high-level features, a CNN-enhanced module is added to improve classification performance. The proposed network is a Sparse Representation (SR) guided deep learning model, which can directly utilize the covariance matrix as the network input, and utilize Riemannian metric to learn geometric structure and sparse features of complex matrices in Riemannian space. Experiments on three real PolSAR datasets demonstrate that the proposed method surpasses state-of-the-art techniques in ensuring accurate edge details and correct region homogeneity for classification.

翻译：深度学习是极化合成孔径雷达(PolSAR)图像分类的一种有效端到端方法，但其缺乏相关数学原理的指导，本质上属于黑箱模型。此外，现有深度模型在欧氏空间中学习特征，通常将PolSAR复数矩阵转换为复值向量作为网络输入，这扭曲了矩阵结构和通道关系。然而，复协方差矩阵是埃尔米特正定(HPD)矩阵，存在于黎曼流形而非欧氏空间中。现有方法无法度量HPD矩阵的几何距离，且因采用不恰当的欧氏度量而易导致误分类。针对这些问题，我们提出一种用于PolSAR图像的新型黎曼稀疏表示学习网络(SRSR CNN)。首先，设计基于超像素的黎曼稀疏表示(SRSR)模型以学习具有黎曼度量的稀疏特征。随后，推导SRSR模型的优化过程并将其展开为SRSRnet，可自动学习稀疏系数与字典原子。此外，为学习上下文高层特征，引入CNN增强模块以提升分类性能。所提网络是稀疏表示(SR)引导的深度学习模型，可直接将协方差矩阵作为网络输入，并利用黎曼度量在黎曼空间中学习复数矩阵的几何结构与稀疏特征。在三个真实PolSAR数据集上的实验表明，该方法在确保精确边缘细节和正确区域同质性方面超越了现有先进分类技术。