Hyperspectral Image Spectral-Spatial Feature Extraction via Tensor Principal Component Analysis
Yuemei Ren, Liang Liao, Stephen John Maybank, Yanning Zhang, Xin Liu
TL;DR
The paper addresses hyperspectral image classification by tackling the challenge of spectral-spatial feature extraction. It introduces a tensor-based framework built on the t-product with circular convolution and extends PCA to Tensor PCA (TPCA), including a fast Fourier-domain implementation that achieves $O(mn)$ complexity. Key contributions include a backward-compatible tensor algebra, a TPCA method that captures spatial relations via tensor covariance, and an empirical demonstration on Indian Pines and Pavia University showing TPCA outperforms traditional PCA and state-of-the-art tensor methods. The work demonstrates that leveraging multi-dimensional tensor structure yields superior spectral-spatial representations and scalable improvements for hyperspectral analysis.
Abstract
This paper addresses the challenge of spectral-spatial feature extraction for hyperspectral image classification by introducing a novel tensor-based framework. The proposed approach incorporates circular convolution into a tensor structure to effectively capture and integrate both spectral and spatial information. Building upon this framework, the traditional Principal Component Analysis (PCA) technique is extended to its tensor-based counterpart, referred to as Tensor Principal Component Analysis (TPCA). The proposed TPCA method leverages the inherent multi-dimensional structure of hyperspectral data, thereby enabling more effective feature representation. Experimental results on benchmark hyperspectral datasets demonstrate that classification models using TPCA features consistently outperform those using traditional PCA and other state-of-the-art techniques. These findings highlight the potential of the tensor-based framework in advancing hyperspectral image analysis.