## 1 Introduction
[PERSON] used different multi-subspaces for the areas to reduce the interference in each area, combined the APG with the patch coordinate descent method, and used the SMSL method to improve the accuracy of heterogeneous background [15]. However, for the infrared images with a complex background, and especially for those that contain clutter signals, as the noise also has a sparse feature as the target, the false alarm rate will increase. For complex scenarios, [PERSON] et al. put forward a non-convex rank approximation minimization (NRAM) detection method for infrared points and moving targets, which introduces extra regular terms into the edges [16]. Although the NRAM method has achieved good results in single image frame detection, the false alarm rate of this method is still high in complex and changing scenarios because it does not consider spatial and temporal information. The above methods only vectorize the infrared image into a matrix, but do not well consider the temporal information. Therefore, many methods on account of the tensor analysis are applied in the IRST system, such as multi-view clustering [17], subspace clustering [18], super-resolution image generation [19], and image video processing [20]. Tensor analysis not only considers the spatial information of image sequences but also the temporal information thereof. First, to fully exploit the inter-frame correlation between infrared image sequences, considering the time consistency and local spatial smoothness between the consecutive frames of the target, we introduced the spatial-temporal tensor into the NRAM model. To obtain more precise background estimations in the detection of infrared points and moving targets, as there was considerable noise in the infrared scenario, the norm was introduced because, compared with the norm, the norm requires not only sparse columns but also sparse rows, which can better remove the strong edge non-target noise. In order to simplify the computational complexity, we introduced the Frobenius norm. Finally, we proposed a minimization of the non-convex spatial-temporal tensor low-rank approximation algorithm (MNSTLA). The main contributions of the MNSTLA model are:  
1. A non-convex spatial-temporal tensor low-rank approximation minimization method for the detection of infrared points and moving targets in the sequence scenarios was proposed. We introduced 3D-TV regularization into the NRAM model. The 3D-TV constraint on the background is helpful for keeping the image details and removing the noise, so it can achieve better detection performance under complex backgrounds. 2. The norm is introduced into the detection of IR points and moving targets to better describe the target components. By combining structured sparsity terms, non-target components, especially those with strong edges, can be eliminated. 3. The ADMM is used to efficiently reduce the computational complexity and solve the low-rank component recovery problem. The paper is organized as follows: in Section 2, the work related to the MNSTLA method-based detection of infrared dim and point targets is briefly described; in Section 3, the proposed MNSTLA model; in Section 4, the extensive experiments carried out on various sequence scenarios are described to illustrate the efficiency of the MNSTLA model, and the results are evaluated subjectively and objectively; and in Section 5, we give the discussion and conclusion.