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.

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