# Spectra-Based Selective Searching for Hyperspectral Anomaly Detection
###### Abstract  
The research on hyperspectral anomaly detection algorithms has become a hotspot, driven by a lot of practical applications, such as mineral exploration, environmental monitoring and the national defense force. However, most existing hyperspectral anomaly detectors are designed with a single pixel as unit, which may not make full use of the spatial and spectral information in the hyperspectral image to detect anomalies. In this paper, to fully combine and utilize the spatial and spectral information of hyperspectral images, we propose a novel spectral-based selective searching method for hyperspectral anomaly detection, which firstly combines adjacent pixels with the same spectral characteristics into regions with adaptive shape and size and then treats those regions as one processing unit. Then, by fusing adjacent regions with similar spectral characteristics, the anomaly can be successfully distinguished from background. Two standard hyperspectral datasets are introduced to verify the feasibility and effectiveness of the proposed method. The detection performance is depicted by intuitive detection images, receiver operating characteristic curves and area under curve values. Comparing the results of the proposed method with five popular and state-of-the-art methods proves that the spectral-based selective searching method is an accurate and effective method to detect anomalies. s +
Footnote †: journal: Medical  
a sliding fixed-size dual-window is employed to select those surrounding pixels as the background pixels of each tested pixel to calculate local background statistics. However, the multivariate Gaussian distribution is too simple to accurately characterize the complicated background of real-world hyperspectral scenes. As a result, a series of modified RX-based anomaly detectors was designed [23; 24; 25; 26; 27]. For example, the covariance matrix of an image was standardized in a regularized-RX detector [25], which could avoid the pathological state of matrix inversion. The kernel-RX (KRX) detector [26] is generally regarded as a nonlinear version of the RX, in which the origin HSI data is mapped to a high-dimensional feature space via the kernel theory to strengthen the differences between anomaly target and background. The cluster-based anomaly detection (CBAD) [27] subdivides the entire image into several clusters, and the RX detector is implemented to detect the anomaly target in each cluster. However, background statistics that are more or less contaminated by anomaly pixels and noise may not effectively characterize the background information. In order to further settle this problem, spectral transform such as fractional Fourier transform (FrFT) [28] were employed for hyperspectral anomaly detection to handle nonstationary noise introduced during the imaging process from satellite or airborne sensors and to extract the intrinsic features of the hyperspectral image. In Ref. [29], the FrFT was applied to process the hyperspectral data, and the original data were transformed to the intermediate domain, including the reflection spectrum and its Fourier transformation information, so that the anomaly target could be clearly distinguished from the background and noise. Then, the RX method achieved better detection performance in this optimal fractional domain. This method is call fractional Fourier entropy (FFE). In Ref. [30], low rank and sparse matrix decomposition (LRaSMD) was utilized to achieve background purification by decomposing the image data into background, noise and anomaly after extracting intrinsic features from the hyperspectral image via FrFT. Then background atoms were selected to build the covariance matrix for Mahalanobis distance-based RX anomaly detection, named feature extraction and background purification anomaly detector (FEBPAD).