## 3 Proposed Algorithm
### Historical Frame Background Extraction Module  
By extracting background information, the tracking algorithm can distinguish between the target and the background more effectively. This helps to reduce the occurrence of false detections and false tracking, especially in scenes with complex backgrounds or high interference in NIR hyperspectral target tracking. And the background information can provide additional contextual information, so that the tracking algorithm can still maintain  
Figure 1: The general structure of the designed algorithm. stable tracking of the target through changes in the background when the target is partially occluded or deformed. In order to obtain rich background information, we build a Historical Frame Background Extraction Module. It is taken into account that images neighboring the current frame in the time dimension contain more information similar to the current frame because they are closer in time. This means that the position and appearance of the target in adjacent frames may be similar because the target usually does not change much over a short period of time. Images farther from the current frame contain more original information because the time interval between them is longer. This means that in farther frames, the location, appearance, etc., of the target change significantly. Therefore, these images contain more raw information that has not been filtered or processed. Therefore, the selected background pool consists of the first four frames relative to the current one, i.e., frames 1, \(t-1\), \(t-3\), and \(t-5\). In HFBE, the missing video frames are interpolated. First, normalize the HSI of the target area \(T^{1}\in R^{B\times W_{T}\times H_{T}}\) in frame 1 and the search area \(S^{t}\in R^{B\times W_{s}\times H_{s}}\) in frame \(t\) (centered on the centroid of the target):  
\[N\big{(}S^{t}_{i}\big{)}=\frac{1}{H_{S}\times W_{S}}\times\sum_{j=1}^{H_{S} \times W_{S}}S^{t}_{ij} \tag{5}\]  
where \(N(\cdot)\) represents the normalization of the HSI of the target area \(S_{t}\), \(S^{i}_{t}\) denotes the \(i\)-th band of the \(t\)-th frame in \(S_{t}\), \(S^{ij}_{t}\) denotes the \(j\)-th pixel of \(S^{i}_{t}\), \(H_{s}\) is the height of \(S_{t}\), and \(W_{s}\) is the width of \(S_{t}\). We use a global spectral curve to represent the spectral information at frame \(t\). The global spectral curve is determined using the following procedure:  
\[C_{g}=\big{\{}C_{gi}\mid C_{gi}=N\big{(}S^{t}_{i}\big{)}\big{\}}_{i\in\{1,\dots,B\}} \tag{6}\]  
where \(C_{g}\) represents the global spectral curve, and \(C_{gi}\) indicates its value at the \(i\)-th spectral band, with \(B\) denoting the total number of bands. The spectral curve represents the spectral response values of a specific point or region across multiple spectral bands, where the horizontal axis denotes the band index, and the vertical axis indicates the normalized pixel value. \(N(S^{i}_{t})\) represents the normalized pixel value of \(S^{i}_{t}\), where \(t\) is a variable indicating the frame index in the hyperspectral video sequence. In the target area of the first frame \(T^{1}\), a small portion of the background is involved in the target area because the target is irregular. In order to accurately find the pixels that best represent the target in a target region containing background pixels, it is necessary to classify the target region based on pixel grayscale values using statistical methods. We consider this method as a statistical approach because it utilizes the statistical properties of the pixel grayscale values in the image for classification. Specifically, we define a quantization process, where the grayscale value of each pixel is mapped to discrete levels, with a parameter \(v_{r}\) controlling the number of levels. In this way, we are able to distinguish between target pixels and background pixels based on the grayscale distribution.