Riemannian Complex Hermit Positive Definite Convolution Network for Polarimetric SAR Image Classification

• URL: http://arxiv.org/abs/2502.08137v2
• Date: Mon, 07 Jul 2025 12:20:28 GMT
• Title: Riemannian Complex Hermit Positive Definite Convolution Network for Polarimetric SAR Image Classification
• Authors: Junfei Shi, Yuke Li, Mengmeng Nie, Fang Liu, Haiyan Jin, Junhuai Li, Weisi Lin,
• Abstract summary: We propose HPDNet, a novel framework that directly processes HPD matrices on the Riemannian manifold.<n>The proposed HPDnet consists of several HPD mapping layers and rectifying layers, which can preserve the geometric structure of the data.<n>A complex LogEig layer is developed to project the manifold data into a tangent space, ensuring that conventional Euclidean-based deep learning networks can be applied to further extract contextual features for classification.
• Score: 40.36326393766876
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep learning has been extensively utilized for PolSAR image classification. However, most existing methods transform the polarimetric covariance matrix into a real- or complex-valued vector to comply with standard deep learning frameworks in Euclidean space. This approach overlooks the inherent structure of the covariance matrix, which is a complex Hermitian positive definite (HPD) matrix residing in the Riemannian manifold. Vectorization disrupts the matrix structure and misrepresents its geometric properties. To mitigate this drawback, we propose HPDNet, a novel framework that directly processes HPD matrices on the Riemannian manifold. The HPDnet fully considers the complex phase information by decomposing a complex HPD matrix into the real- and imaginarymatrices. The proposed HPDnet consists of several HPD mapping layers and rectifying layers, which can preserve the geometric structure of the data and transform them into a more separable manifold representation. Subsequently, a complex LogEig layer is developed to project the manifold data into a tangent space, ensuring that conventional Euclidean-based deep learning networks can be applied to further extract contextual features for classification. Furthermore, to optimize computational efficiency, we design a fast eigenvalue decomposition method for parallelized matrix processing. Experiments conducted on three real-world PolSAR datasets demonstrate that the proposed method outperforms state-of-the-art approaches, especially in heterogeneous regions.

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