Recently, deep learning methods have achieved superior performance for Polarimetric Synthetic Aperture Radar(PolSAR) image classification. Existing deep learning methods learn PolSAR data by converting the covariance matrix into a feature vector or complex-valued vector as the input. However, all these methods cannot learn the structure of complex matrix directly and destroy the channel correlation. To learn geometric structure of complex matrix, we propose a Riemannian complex matrix convolution network for PolSAR image classification in Riemannian space for the first time, which directly utilizes the complex matrix as the network input and defines the Riemannian operations to learn complex matrix's features. The proposed Riemannian complex matrix convolution network considers PolSAR complex matrix endowed in Riemannian manifold, and defines a series of new Riemannian convolution, ReLu and LogEig operations in Riemannian space, which breaks through the Euclidean constraint of conventional networks. Then, a CNN module is appended to enhance contextual Riemannian features. Besides, a fast kernel learning method is developed for the proposed method to learn class-specific features and reduce the computation time effectively. Experiments are conducted on three sets of real PolSAR data with different bands and sensors. Experiments results demonstrates the proposed method can obtain superior performance than the state-of-the-art methods.

翻译：最近，深度学习方法在极化合成孔径雷达（PolSAR）图像分类中取得了卓越性能。现有深度学习方法通过将协方差矩阵转换为特征向量或复值向量作为输入来学习PolSAR数据。然而，这些方法均无法直接学习复矩阵的结构，且破坏了通道相关性。为学习复矩阵的几何结构，我们首次在黎曼空间中提出了一种用于PolSAR图像分类的黎曼复矩阵卷积网络，该网络直接以复矩阵作为网络输入，并定义黎曼操作以学习复矩阵的特征。所提出的黎曼复矩阵卷积网络将PolSAR复矩阵视为内嵌于黎曼流形的结构，并在黎曼空间中定义了一系列新的黎曼卷积、ReLu和LogEig操作，突破了传统网络的欧几里得约束。随后，附加一个CNN模块以增强上下文黎曼特征。此外，针对所提方法开发了一种快速核学习技术，用于学习类别特定特征并有效降低计算时间。在三组不同波段和传感器的真实PolSAR数据上进行了实验。实验结果表明，所提方法能够获得优于现有最先进方法的性能。