Riemannian Nearest-Regularized Subspace Classification for Polarimetric SAR Images

The nearest regularized subspace (NRS) algorithm is a kind of effective representation learning method, which can obtain both accuracy and speed for polarimetric synthetic aperture radar (PolSAR) image classification. However, existing NRS methods use the polarimetric feature vector instead of the Pol-SAR original coherency matrix (known as the Hermitian positive definite (HPD) matrix) as the input. This will destroy the matrix structure and miss the instinct correlation among channels. How to utilize the original coherency matrix to the NRS method is a key problem. To address this limitation, a Riemannian NRS (RNRS) method is proposed, which considers the HPD matrices endowed in a Riemannian space. First, to utilize the PolSAR original data, an RNRS method is proposed by constructing HPD dictionary and HPD distance metric. Then, a new Tikhonov regularization term is designed to reduce the differences within the same class. Finally, the optimization method is developed to resolve the proposed model, and the first-order derivative is inferred. Besides, only coherency matrix T is used as the input in the proposed method, while multiple features are utilized for compared methods in the experiments. Experimental results demonstrate that the proposed method can outperform the state-of-the-art algorithms even with fewer features.