Separable Spatial–Temporal Patch-Tensor Pair Completion for Infrared Small Target Detection

The infrared small target detection (IRSTD) task presents significant challenges due to low signal-to-clutter ratio, complicated background, and strong interferences. While tensor theory has shown promise in detection performance, three issues regarding damaged tensor construction, inaccurate tensor models, and high computation complexity remain. This study addresses these issues by introducing an independent spatial-temporal perspective, and proposes a fast and separable spatial-temporal tensor completion model. A new tensor structure named separable spatial-temporal patch-tensor pair (SSPP) is conceived to alleviate the dilemma of maintaining neighborhood structure and temporal consistency when constructing image tensors. By treating spatial and temporal dimensions as independent, SSPP enables flexible distribution hypotheses and representations in each dimension. Two tensor models are devised: the spatial model focuses on target enhancement in the spatial dimension, while the temporal one concentrates on suppressing strong interference in the temporal dimension. A long-term memory regularization is further introduced to the temporal model for target movement perception, enhancing its robustness to interferences. By combining these tensor models and employing a coarse-to-fine detection strategy, our method offers an effective solution for IRSTD. Extensive experiments on practical datasets have demonstrated the superiority of the proposed method in terms of target enhancement, background suppression, and detection efficiency.