# Riemannian Complex Matrix Convolution Network for PolSAR Image Classification

arXiv: https://arxiv.org/abs/2312.03378 · HTML: https://mlsanity.com/paper/2312.03378/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 6 Dec 2023.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices](https://mlsanity.com/paper/1507.02772/) (2015)
- [Polarimetric Convolutional Network for PolSAR Image Classification](https://mlsanity.com/paper/1807.02975/) (2018)
- [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)
- [Riemannian kernel based Nystr"om method for approximate infinite-dimensional covariance descriptors with application to image set classification](https://mlsanity.com/paper/1806.06177/) (2018)
- [A PolSAR Scattering Power Factorization Framework and Novel Roll-Invariant Parameters Based Unsupervised Classification Scheme Using a Geodesic Distance](https://mlsanity.com/paper/1906.11577/) (2019)
- [Multi-frequency PolSAR Image Fusion Classification Based on Semantic Interactive Information and Topological Structure](https://mlsanity.com/paper/2209.01921/) (2022)

## Built on by (most cited first, 1 of 1)

- [Classification of Buried Objects from Ground Penetrating Radar Images by using Second Order Deep Learning Models](https://mlsanity.com/paper/2410.07117/) (2024)

## Abstract (arXiv)

Recently, deep learning methods have achieved superior performance for Polarimetric Synthetic Aperture Radar(PolSAR) image classification. Existing deep learning methods learn PolSAR data by converting the covariance matrix into a feature vector or complex-valued vector as the input. However, all these methods cannot learn the structure of complex matrix directly and destroy the channel correlation. To learn geometric structure of complex matrix, we propose a Riemannian complex matrix convolution network for PolSAR image classification in Riemannian space for the first time, which directly utilizes the complex matrix as the network input and defines the Riemannian operations to learn complex matrix's features. The proposed Riemannian complex matrix convolution network considers PolSAR complex matrix endowed in Riemannian manifold, and defines a series of new Riemannian convolution, ReLu and LogEig operations in Riemannian space, which breaks through the Euclidean constraint of conventional networks. Then, a CNN module is appended to enhance contextual Riemannian features. Besides, a fast kernel learning method is developed for the proposed method to learn class-specific features and reduce the computation time effectively. Experiments are conducted on three sets of real PolSAR data with different bands and sensors. Experiments results demonstrates the proposed method can obtain superior performance than the state-of-the-art methods.