## 2 Background and Basic Principle
### Analysis of Target-Complex Background Coupling  
Background clutter and noise may interfere with the radiative diffusion of the target energy signal, causing changes in the energy distribution, which are described here as the result of the interaction between the target and the background. The interaction between the target and the background is mainly reflected in the spatial and temporal changes in energy and distribution, including changes in the energy value in the image element when the background is occluded by the target and changes in the local area perturbation due to the target entering different background regions [17]. The SCR used to evaluate weak targets in complex scenes is based on the difference between the target and the background, defined as follows [18]:  
\[\text{SCR}=\frac{\mu_{T}-\mu_{B}}{\sigma_{B}} \tag{15}\]  
In this equation, \(\mu_{T}\) and \(\mu_{B}\) refer to the average grayscale signal of the target and background regions, respectively, and \(\sigma_{B}\) is the standard deviation of the grayscale signal of the background region. The standard evaluation of the signal-to-heterodyne ratio places the background in the global field of view and ignores local significance [19]. Therefore, a localized signal-to-heterodyne ratio is introduced on top of the signal-to-heterodyne ratio, which describes the difference between the target and the background in a localized region [20]:  
\[\text{LSCR}=\frac{\mu_{T}-\mu_{LB}}{\sigma_{LB}} \tag{16}\]  
In this equation, \(\mu_{LB}\) refers to the average grayscale signal of the background region within a specified range L near the target and \(\sigma_{LB}\) is the standard deviation of the grayscale signal of the corresponding background region. The Target Significant Rate (TSR) is a statistical parameter that reflects the significance of the target in the whole scene; generally speaking, the value of the TSR is between 0 and 1, and when the TSR equals 1, it indicates that the target has the highest energy in the whole scene:  
\[\text{TSR}=\exp(\frac{\mu_{T}-\mu_{B}}{\text{max}(B)-\mu_{B}}-1) \tag{17}\]  
In this equation, \(\text{max}(B)\) is the maximum gray value within the global background region B. In summary, for the optical data of any scene, the following target feature vectors are adopted in this paper as the main quantitative metrics for target saliency assessment as follows:  
\[\text{TF}=[\text{TSR},\text{SCR},\text{LSCR}] \tag{18}\]  
Figure 2 shows a schematic of the signal information of a typical target in a real scenario. The first step of target detection in a complex scene is to identify all regions of interest in the image, including the actual target region, as well as interfering regions that are similar to the target. These interfering regions show high feature similarity with the actual target, which may lead to confusion when recognizing the real target. In this study, a target-confusion-element assessment metric is proposed in anticipation of assessing the degree of difficulty of target detection from the perspective of confusable elements [21]. The short-time Fourier transform can be used to analyze local signals with the help of a window. The Gabor transform is a type of short-time Fourier transform, and by introducing a Gaussian window, the spectral characteristics of a signal can be analyzed within a specific window range. The energy distribution of a weak target consists of its energy and morphological characteristics, and Gabor filtering in a fixed direction not only maintains the energy structure of the target in a specific direction but also enhances the specific frequency content in that direction while suppressing other frequency components. Here, the use of the Gabor transform for null domain filtering allows for the enhancement of point-like structures similar to the target while preserving significant edge and texture  
Figure 2: Typical target information in real-world scenarios (**a–d**).