  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.
