## 1 Introduction  
The infrared detection system has the advantages of not being affected by light and, therefore, being capable of working at all times of the day [1]; not emitting electromagnetic waves and, therefore, being a system using a non-automatic detection method [2]; and having a strong penetrability and, therefore, being capable of penetrating the covers of dust, clouds, and smoke so as to better identify false camouflage targets, making it an effective supplement or substitute for the traditional visible light detection system and the radar detection system [3]. Therefore, the infrared point and moving target detection on account of the infrared detection system has always been an important topic and hotspot of research. The infrared images have a low rank feature due to the many repetitive elements in the background, and they have a sparse feature due to the few feature points of infrared points and moving targets [4; 5]. In this case, the detection of infrared points and moving targets is transformed into a classification task on account of the good performance of sparse representation in the classification task, which is what the method on of low-rank sparse is concerned about. A sparse representation-based multispectral image target detection method was first proposed by the US Army Sensor Research Laboratory in 2014 [6]. He adopted the augmented Lagrange multiplier method to perform the optimization on account of the SR theory and the low-rank matrix [7] in 2015 based off the LRSR mode. This method can detect dim and point targets in a background with strong noise but does not have a good background suppression effect. To overcome the limitations of conventional methods, [PERSON] put forward an IPI (Infrared Patch-Image) model on account of the image segmentation by means of a sliding window, and the method can detect dim and point targets according to the targeted sparse feature of each patch image [8]. Considering the non-local autocorrelation structure for the background, the assumptions of the infrared patch image (IPI) model are in excellent agreement with the true scenario, which rephrases:  
\[D_{P}=B_{P}+T_{P}+N_{P} \tag{1}\]  
where \(D_{P}\), \(B_{P}\), \(T_{P}\), and \(N_{P}\) are patch-images corresponding to the original, background, target, and random noise images, which are shown separately. Furthermore, the features of low-rank for the background \(B\), and the target \(T\), which is sparsity. [PERSON] et al. of Nanjing University introduced a structural prior model into the detection process of infrared points and moving targets, namely WIPI (Weighted Infrared Patch-Image). This method can better preserve the infrared point and moving targets while suppressing the strong edges [9]. [PERSON] proposed an RIPT model. Furthermore, in view of the detection of infrared points and moving targets with insufficient prior information and strong edges [10], the SNN is used to separate the real target from the background by combining the non-local and local spatial priors. In order to solve the problems that the observation values of strong edge information are insufficient and the implicit assumptions do not match, The NIPPS model put forward by [PERSON], which can detect the residual error in the target image and is used for singular values [11]. As the SNN is not a convex envelope of low-rank background, and in view of the fact that the traditional IPT method only uses spatial information, [PERSON] proposed the WNRIPT model [12]. In order to adapt to different images and solve the problem of images with strong edges, [PERSON] used adaptive weights and an augmented Lagrange multiplier method [13]. [PERSON] put forward an IPI model-based detection method for infrared point and moving targets, which maintains the spatial correlation among images, constructs a patch image form, and uses the ADMM multiplier method to optimize the solution finding so as to deal with the non-smooth and non-uniform background by the TV-PCP method [14].