## 1 Introduction
applied the RCTV method to small target detection in infrared image sequences [18], improving detection efficiency. [PERSON] proposed a novel approach based on multi-subspace learning and spatial-temporal tensor data structures [19]. [PERSON] introduced a new Long-term Spatial-Temporal Tensor (LSTT) model, employing image registration techniques to achieve frame-to-frame alignment and constructing a new image tensor through direct superposition of aligned frames [20]. [PERSON] developed a four-dimensional tensor model based on superpixel segmentation and statistical clustering for infrared dim target detection [21], further enhancing the spatial structural correlations among image patches. [PERSON] proposed a novel IPT model (termed IPT-TCTV), constructing an improved Spatial-Temporal Tensor (STT) model through sliding 3-D windows, which better preserves the spatial correlation and temporal continuity of multi-frame infrared images in the constructed tensor [22]. [PERSON] introduced a new 3-D paradigm framework that incorporates spatial-temporal weighting and regularization into the low-rank sparse tensor decomposition model [23]. [PERSON] developed an iterative corner and edge weighting method based on tensor decomposition, designing corner intensity as the weight for target components and edge intensity as the weight for interference components, enabling more accurate separation of targets and interference [24]. These are excellent methods proposed in recent years, capable of preserving the characteristics of the original image sequences during tensor construction and calculating target weights from the original image, demonstrating strong performance in small target detection for single-aperture infrared image sequences. However, they are not well suited for leveraging the unique features of bio-inspired infrared compound eye images. This paper proposes a low-rank and sparse decomposition method based on the image characteristics of bio-inspired infrared compound eyes. The method reconstructs the structural tensor of our infrared compound eye images according to their features. Initially, the entire compound eye image is segmented to retain the images of the ommatidia regions. These ommatidia images are then arranged into a tensor along the temporal dimension based on their size and number. A compound eye structural weighting operator is designed to integrate information from all ommatidia images, effectively utilizing the scene correlation between adjacent ommatidia and the scene variability due to different imaging angles. We combine RCTV (Representative Coefficient Total Variation) and a reweighted \(l_{1}\)-norm that incorporates the compound eye structural weights into a novel model. This model imposes TV regularization constraints on the representative coefficients to enhance computational efficiency and employs the compound eye structural weighting operator to improve the accuracy of target detection, enabling rapid and accurate detection of small infrared targets. Quantitative and qualitative experiments demonstrate that, compared to other methods, this approach offers significant advantages in quickly detecting small targets in infrared compound eye images and effectively suppressing background clutter.