Hyperspectral Anomaly Detection by Fractional Fourier Entropy

Anomaly detection is an important task in hyperspectral remote sensing. Most widely used detectors, such as Reed–Xiaoli (RX), have been developed only using original spectral signatures, which may lack the capability of signal enhancement and noise suppression. In this article, an effective alternative approach, fractional Fourier entropy (FrFE)-based hyperspectral anomaly detection method, is proposed. First, fractional Fourier transform (FrFT) is employed as preprocessing, which obtains features in an intermediate domain between the original reflectance spectrum and its Fourier transform with complementary strengths by space-frequency representations. It is desirable for noise removal so as to enhance the discrimination between anomalies and background. Furthermore, an FrFE-based step is developed to automatically determine an optimal fractional transform order. With a more flexible constraint, i.e., Shannon entropy uncertainty principle on FrFT, the proposed method can significantly distinguish signal from background and noise. Finally, the proposed FrFE-based anomaly detection method is implemented in the optimal fractional domain. Experimental results obtained on real hyperspectral datasets demonstrate that the proposed method is quite competitive.