## 1 Introduction
This is reflected in the compound eye images as targets exhibiting different sizes and responses across ommatidia. Detecting all small targets appearing in the ommatidia is essential to further combine their geometric information for estimating target distance ranges. Infrared small target detection methods can be categorized into model-based approaches and deep learning-based approaches broadly. Due to the wide field of view and low pixel resolution of individual ommatidia in our infrared compound eye camera, it is challenging to obtain detailed features. Therefore, within the model-based framework, we employ Low-Rank and Sparse Decomposition (LRSD) for small target detection. The LRSD-based method assumes that infrared images consist of low-rank background signals, sparse target signals, and noise signals [6; 7]. Specifically, in infrared imaging, some image patches in the background are approximately linearly correlated, indicating that the background satisfies the low-rank property. For targets, due to the considerable distance between the real targets and the imaging system, the targets occupy only a few pixels in the entire infrared image, making the target component sparse relative to the whole image [7]. By performing low-rank and sparse decomposition on the original infrared image, the low-rank and sparse components are separated, with the sparse component corresponding to the target. Applying threshold segmentation to the sparse component enables target detection. Based on the aforementioned assumptions, [PERSON] et al. [7] initially developed an Infrared Patch-Image (IPI) model for infrared small target detection. However, when dealing with non-smooth backgrounds, the IPI model results in target images with strong edge residuals. Consequently, numerous improved algorithms have been proposed based on IPI, such as the Non-negative Infrared Patch-Image model via Partial Sum Minimization of Singular Values (NIPPS) proposed by [PERSON] et al. [8], and the approach by [PERSON] and [PERSON] [9; 10], which employs a non-convex \(\gamma\)-norm to constrain the background. This not only overcomes the limitations of the nuclear norm in the IPI model but also achieves higher detection speeds, while using the \(l_{2,1}\)-norm to constrain sparse edges with approximately linear structures. [PERSON] et al. [11] were the first to extend the low-rank and sparse decomposition-based infrared small target detection algorithm from two-dimensional matrices to three-dimensional tensors, proposing the Reweighted Infrared Patch Tensor (RIPT) model. Following this tensor construction scheme, [PERSON] and [PERSON] [12] utilized the Partial Sum of the Tensor Nuclear Norm (PSTNN) to constrain the low-rank component and effectively suppress the background. [PERSON] et al. [13] employed the Tensor Fiber Nuclear Norm and Hyper Total Variation (TV, Log TFNN) to suppress both background and noise. Figure 1: Typical examples of infrared small targets in real scenes [5]. (This small target is a flying object). In image sequences, the background exhibits low-rank properties in the temporal domain, while the target is sparsely distributed in the temporal domain [14]. To leverage the spatial-temporal correlations in infrared image sequences, [PERSON] et al. [15] extended the IPI model from the spatial domain to the spatial-temporal domain. In recent years, many scholars have explored various methods, each with its distinct advantages. For instance, [PERSON] et al. [16] proposed a Non-convex Tensor Low-rank Approximation (NTLA) with Asymmetric Spatial-Temporal Total Variation (ASTTV) to enhance target detection capabilities. Meanwhile, [PERSON] et al. constructed a four-dimensional infrared tensor from a series of infrared images and decomposed it into low-dimensional tensors using the Tensor Train (TT) technique and its extension, Tensor Ring (TR) [17], while preserving the spatial structural features and temporal characteristics of the original data. [PERSON] et al.