## 1 Introduction
In addition to the sparse representation method, the collaboration representation detector (CRD) [23] has been proven to be simpler and more efficient, directly employing the neighboring pixels of the testing pixel within a sliding dual-window as the background dictionary and paying close attention to the collaboration among dictionary atoms. An \(l_{2}\)-norm-constrained coefficient vector is imposed to allow all of the atoms in the dictionary to participate in representation. However, the performance of CRD is unsatisfactory when the dual-window sizes are inappropriate, which are heavily dependent on the size of abnormal targets [23]. In the absence of prior information, it is difficult to set appropriate dual-window sizes [26] to ensure the purity of the background dictionary [27]. Furthermore, only local information attributes to the constraint weight vector and the global structure information of the image are disregarded, which limits the performance of the CRD as well. To improve detection accuracy, a collaborative-representation-based with outlier removal anomaly detector (CRBORAD) [28; 29] has been proposed for purifying the background dictionary by eliminating some pixels with a small probability in the Gaussian distribution of neighborhood pixels. However, it is necessary to consider the actual situation that may not conform to statistical laws. The kernel method is also applied in CRD to improve its detection performance by projecting linearly inseparable data into a high-dimensional feature space in which those data become more separable [30; 31]. Through the recursion between the kernel covariance matrices at the last and the current moments, as well as the detection values directly imposed on the regularized matrix instead of the kernel operations, repeated calculation is avoided and the overall computational complexity reduces, which was proposed in [32] and named real-time kernel CRD (RT-KCRD). A morphology-based collaborative representation detector (MCRD) [33] has been proposed to increase the incorporation of global spatial information of HSI by applying morphological filters. Each morphological profile (MP) is repeatedly acquired from each principal component of the data, which greatly increases computational complexity and running time. In [25], 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 the linear representation and detection performance. However, this came at the cost of increased computational complexity and time, which is called local summation anomaly detection based on collaborative representation and inverse distance weight. Furthermore, the importance uniformity of different bands was broken in [34] by a self-weighted collaborative representation-based detector (SWCRD). Weight learning and collaborative representation are combined into a joint objective function to assign suitable weights to each band and simultaneously achieve collaborative representation, resulting in the improvement of anomaly detection of CRD. In this paper, a selective search collaborative representation detector (SSCRD) is proposed to improve the anomaly detection capability and robustness of CRD, which not only effectively improves anomaly detection performance, but also avoids the sensitivity of detection accuracy on the size of the dual-window by taking global spatial information into consideration. First, a selective search is applied to HSI, in which adjacent pixels with similar spectral features are fused into several regions of variable size. The regions that occupy most of the pixels can be considered as the background, and the remaining small regions have a high probability of being abnormal. A selective search realizes the preliminary judgment of whether the pixels in an HSI are background or abnormal.