Hyperspectral anomaly detection via fractional Fourier transform and deep belief networks

Abstract

Nowadays, deep learning (DL) theory-based algorithms have been developed in anomaly detection (AD) for hyperspectral image (HSI) and verified to be very effective. Deep belief networks (DBNs) are important content in DL research. The fractional Fourier domain (FrFD) is between the original spectral domain and its Fourier transform domain. In the FrFD, signal can be enhanced, and noise can be suppressed. A novel fractional Fourier transform and deep belief networks (FDBN)-based anomaly detection (AD) algorithm is proposed in this article. The FDBN algorithm has two parts and takes advantage of both the spatial and spectral characteristics of the test HSI. For the spatial characteristics, the tensor block centered on each test point is first transformed into one-dimensional vector, and a higher dimensional dataset with more spatial information is obtained. DBNs are then used for dimensionality reduction (DR) and removing redundant information. After that, the dataset obtained by DBN is transformed by fractional Fourier transform (FrFT), and modified tensor projection (MTP) is used. For the spectral characteristics, the original HSI is first subjected to FrFT. Then, in the fractional Fourier domain (FrFD), the reconstruction error between the test point and its DBNs reconstruction model is obtained. For the proposed FDBN, the above the spatial and spectral characteristics are combined by the weight coefficient. In the experimental section, the effectiveness of FDBN is verified through four comparison algorithms in four HSIs.