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

arXiv: https://arxiv.org/abs/2502.08137 · HTML: https://mlsanity.com/paper/2502.08137/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 55 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Builds on (most cited first, 9 of 9)

- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [UIU-Net: U-Net in U-Net for Infrared Small Object Detection](https://mlsanity.com/paper/2212.00968/) (2022)
- [Towards Faster Training of Global Covariance Pooling Networks by Iterative Matrix Square Root Normalization](https://mlsanity.com/paper/1712.01034/) (2017)
- [Riemannian Local Mechanism for SPD Neural Networks](https://mlsanity.com/paper/2201.10145/) (2022)
- [A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matrices](https://mlsanity.com/paper/1805.11204/) (2018)
- [SAAN: Similarity-aware attention flow network for change detection with VHR remote sensing images](https://mlsanity.com/paper/2308.14570/) (2023)
- [VTAE: Variational Transformer Autoencoder with Manifolds Learning](https://mlsanity.com/paper/2304.00948/) (2023)
- [Multiple Riemannian Manifold-valued Descriptors based Image Set Classification with Multi-Kernel Metric Learning](https://mlsanity.com/paper/1908.01950/) (2019)
- [Riemannian Nearest-Regularized Subspace Classification for Polarimetric SAR images](https://mlsanity.com/paper/2201.00337/) (2022)

## Abstract (arXiv)

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.