Hyperspectral Anomaly Detection Using Reconstruction Fusion of Quaternion Frequency Domain Analysis

Most existing techniques consider hyperspectral anomaly detection (HAD) as background modeling and anomaly search problems in the spatial domain. In this article, we model the background in the frequency domain and treat anomaly detection as a frequency-domain analysis problem. We illustrate that spikes in the amplitude spectrum correspond to the background, and a Gaussian low-pass filter performing on the amplitude spectrum is equivalent to an anomaly detector. The initial anomaly detection map is obtained by the reconstruction with the filtered amplitude and the raw phase spectrum. To further suppress the nonanomaly high-frequency detailed information, we illustrate that the phase spectrum is critical information to perceive the spatial saliency of anomalies. The saliency-aware map obtained by phase-only reconstruction (POR) is used to enhance the initial anomaly map, which realizes a significant improvement in background suppression. In addition to the standard Fourier transform (FT), we adopt the quaternion FT (QFT) for conducting multiscale and multifeature processing in a parallel way, to obtain the frequency domain representation of the hyperspectral images (HSIs). This helps with robust detection performance. Experimental results on four real HSIs validate the remarkable detection performance and excellent time efficiency of our proposed approach when compared to some state-of-the-art anomaly detection methods.