A Lightweight Riemannian Covariance Matrix Convolutional Network for PolSAR Image Classification

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, learning features in Euclidean space. However, it is well-known that covariance matrices are manifold data endowing in Riemannian space instead of Euclidean space. Existing methods cannot learn the geometric characteristics of covariance matrices directly and destroy the channel correlation. To learn features from covariance matrices directly, we propose a lightweight Riemannian covariance matrix convolutional network (LRCM_CNN) for PolSAR classification for the first time, which directly utilizes the covariance matrix as the network input and defines the Riemannian operations to learn complex matrix's features in Riemannian space. The proposed LRCM_CNN network initially designs a lightweight Riemannian covariance matrix network (LRCMnet) to learn covariance matrix features by exploiting a series of Riemannian convolution, rectified linear unit (ReLu), and LogEig operations in Riemannian space, which breaks through the Euclidean constraint of conventional networks. Then, features learned from covariance matrices are converted from Riemannian to Euclidean space, and a CNN module is appended to enhance contextual covariance matrix features. Besides, a fast kernel learning method is developed for the proposed method to learn class-specific features and reduce the computation time effectively, which implements the lightweight RCMnet. Experiments are conducted on four sets of real PolSAR data with different bands and sensors. Experiments results demonstrate the proposed method can obtain superior performance than the state-of-the-art methods.