# Spectra-Based Selective Searching for Hyperspectral Anomaly Detection
###### Abstract
In addition to the above Gaussian model-based detector, some robust statistic modeling detectors have been developed, including the discriminative metric learning-based anomaly detector [31], random-selection-based model [32], and nonlinear learning-based detection method [33]. These anomaly detectors construct background statistics through different strategies, thereby avoiding contamination of background statistics by abnormal pixels. However, it is still difficult to secure satisfactory anomaly detection performance when processing images with complex backgrounds. Apart from the aforementioned statistical strategy-based detection methods, geometrical strategy-based detection methods have recently gained much attention. This strategy usually considers that the background pixels can be approximated as a certain combination of a group of primary spectra extracted from HSI data, while the anomaly target is exceptional and cannot be reconstructed with those primary spectra. For instance, in the subspace-based detector [34], a low-dimension feature space considered as a collection of background spectra is constructed by a linear transformation from the HSI data cube. The representation residual of test pixels can be calculated by projecting all the pixels onto the background orthogonal subspace and then used for anomaly detection. Sparse representation and collaborative representation [35; 36; 37] have been recently used for anomaly detection of hyperspectral images. In the low-rank and sparse representation (LRASR) detector [38], the low-rank representation is applied to model the background, while a sparsity-induced regularization term is appended to the representation coefficients matrix which contains the background information. K-means is used to select the background dictionary's atoms from HSI data cube. The principle of the collaborative representation-based detector (CRD) [39] is that each background pixel can be approximately represented by its spatial surrounding pixels in a sliding size-fixed local dual-window with the form of linear combinations, while anomalies cannot. The \(\ell_{2}\)-norm minimization of the representation weight vector is employed to enhance the collaboration among these pixels. By subtracting the predicted background result from the origin HSI data, a residual image can be obtainedto reveal the anomaly pixels. However, regardless of the sparse representation-based detector or collaborative representation-based detector, the performance of those detectors highly depends on the background dictionary that is chosen. If the background dictionary is inexact or contaminated by anomalies, the detection performance may deteriorate. This means that the background dictionary extracted in sparse representation needs to be as accurate and complete as possible, and the size of the dual windows is one of the most critical factors in collaborative representation. In Ref. [40], the various local spatial distribution information of the neighboring pixels of a test pixel were considered by adding a summation strategy to the local window in the CRD algorithm, which improved the accuracy of linear representation and the detection performance, but this came at the cost of increased computational complexity and time, called local summation anomaly detection based on collaborative representation and inverse distance weight (LSAD-CR-IDW). In this paper, to fully combine and utilize the spatial and spectral information of hyperspectral images and to implement hyperspectral anomaly detection, a spectra-based selective searching (Triple-S) hyperspectral anomaly detection algorithm is proposed. Unlike most existing algorithms, the adaptive regions composed of adjacent pixels with the same spectral characteristics are referred to as the processing unit rather than a single pixel. In addition to the differences between the anomalies and the background, similar properties among the anomaly pixels and among the background pixels are exploited in the proposed detector via two phases: oversegmentation and region merging.