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Addressing the problems of visual surveillance for anti-UAV, a new flying small target detection method is proposed based on Gaussian mixture background modeling in a compressive sensing domain and low-rank and sparse matrix decomposition of local image. First of all, images captured by stationary visual sensors are broken into patches and the candidate patches which perhaps contain targets are identified by using a Gaussian mixture background model in a compressive sensing domain. Subsequently, the candidate patches within a finite time period are separated into background images and target images by low-rank and sparse matrix decomposition. Finally, flying small target detection is achieved over separated target images by threshold segmentation. The experiment results using visible and infrared image sequences of flying UAV demonstrate that the proposed methods have effective detection performance and outperform the baseline methods in precision and recall evaluation.