Riemannian Complex Hermit Positive Definite Convolution Network for Polarimetric SAR Image Classification
Journal:
arXiv
Published Date:
Feb 12, 2025
Abstract
Deep learning can learn high-level semantic features in Euclidean space
effectively for PolSAR images, while they need to covert the complex covariance
matrix into a feature vector or complex-valued vector as the network input.
However, the complex covariance matrices are essentially a complex Hermit
positive definite (HPD) matrix endowed in Riemannian manifold rather than
Euclidean space. The matrix's real and imagery parts are with the same
significance, as the imagery part represents the phase information. The matrix
vectorization will destroy the geometric structure and manifold characteristics
of complex covariance matrices. To learn complex HPD matrices directly, we
propose a Riemannian complex HPD convolution network(HPD\_CNN) for PolSAR
images. This method consists of a complex HPD unfolding network(HPDnet) and a
CV-3DCNN enhanced network. The proposed complex HPDnet defines the HPD mapping,
rectifying and the logEig layers to learn geometric features of complex
matrices. In addition, a fast eigenvalue decomposition method is designed to
reduce computation burden. Finally, a Riemannian-to-Euclidean enhanced network
is defined to enhance contextual information for classification. Experimental
results on two real PolSSAR datasets demonstrate the proposed method can
achieve superior performance than the state-of-the-art methods especially in
heterogeneous regions.
