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Infrared point-target detection is one of the key technologies in infrared guidance systems. Due to the long observation distance, the point target is often submerged in the background clutter and large noise in the process of atmospheric transmission and scattering, and the signal-to-noise ratio is low. On the other hand, the target in the image appears in the form of fuzzy points, so that the target has no obvious features and texture information. Therefore, scholars have proposed many object detection methods for dimming infrared images, which has become a hot research topic on account of the flow-rank model based on the image patch. However, the result has a high false alarm rate because the most low-rank models based on the image patch do not consider the spatial-temporal characteristics of the infrared sequences. Therefore, we introduce 3D total variation (3D-TV) to regularize the foreground on account of the non-convex rank approximation minimization method, so as to consider the spatial-temporal continuity of the target and effectively suppress the interference caused by dynamic background and target movement on the foreground extraction. Finally, this paper proposes the minimization of the non-convex spatial-temporal tensor low-rank approximation algorithm (MNSTLA) by studying the related algorithms of the point infrared target detection, and the experimental results show strong robustness and a low false alarm rate for the proposed method compared with other advanced algorithms, such as NARM, RIPT, and WSNMSTIPT. Full article