Hyperspectral Anomaly Detection Using a Quaternion Matrix of Wavelet Transform

Dimensionality reduction (DR) as a standard preprocessing method is used to remove the spectral redundancy of hyperspectral images (HSIs). However, HSIs after DR will still contain residual redundant and noise information. After DR, how to preserve the main information while further removing redundant and noise information is an effective means to improve the accuracy of subsequent image processing. Wavelet transform (WT) can provide a method for analyzing multi-scale or multi-resolution signals and divide HSIs into low-frequency sub-images and high-frequency sub-images, which correspond exactly to background information and anomaly information. In addition, noise and redundant information are mainly present in high-frequency sub-images. In this paper, a quaternion matrix of WT is proposed for hyperspectral anomaly detection (HAD). First, the optimal clustering framework (OCF) is used to reduce dimensionality and eliminate spectral redundancy for the original HSI, which can avoid modifying the original data and make the data used more reliable. To better process the background and anomalous information of HSIs respectively, the HSI after OCF is then transformed into eight sub-images through a layer of 3-D wavelet decomposition. To remove residual redundancy and noise information in HSIs after DR, the four sub-images with high frequency in the spectral dimension are replaced by quaternion matrices respectively and the new eight sub-images are subjected to wavelet inverse transform (WIT). Furthermore, to better suppress background information and highlight anomaly points, the dataset after WIT is reconstructed through the stacked autoencoder (SAE). Finally, to better utilize spatial information, tensor RX (TRX) is used on the SAE reconstruction difference. The experiments on five real HSIs show that the overall performance of the proposed QMWT is superior to seven comparison algorithms.