## 3 Spatial Enhanced Detection Algorithm
### Local Uncertainty Measurement  
In this paper, an uncertainty measurement method based on a local-component-consistency-evaluation assignment for target signal enhancement is proposed to help distinguish the target from the background. The uncertainty measurement is conducted in two steps: First, a confidence assignment function is constructed based on the results of the local component consistency evaluation. Then, the local component uncertainty of the image is measured according to the feature consistency of the local region of the image. Similar to methods inspired by the human visual system, the LUM can be calculated by sliding a window. The size of the sliding window is determined by the center window; the optimal size of the center window should be able to wrap the target signal, with the complete window structure being 5 \(\times\) 5 in size. By adjusting the size of the center window, one can effectively deal with different sizes and shapes of the target. In a complex background, there are different characteristics between the target and background and different types of backgrounds. Assume that a small window containing only similar-image background signals is relatively stable when the following occurs:  
1. When the window only covers the background signal, the local gray value is stable and the consistency is high;
2. When the target signal is wrapped in the window, the local gray value is also relatively stable, but the energy in the window should be significantly higher than that in the background area;
3. When the window-wrapping target is at the interface with the background, the local gray value has an obvious gradient and low consistency. In this paper, a local signal's gray consistency evaluation standard is defined, which is used to evaluate the signal component consistency between the central region and the surrounding eight neighborhood regions:  
\[LC_{ij}=\frac{G_{ij}^{0}}{LB_{ij}}\times\frac{G_{ij}^{0}}{\max\left(G_{ij}^{ k}\right)} \tag{31}\]  
\[LB_{ij}=\frac{1}{K}\sum_{k=1}^{K}G_{ij}^{k} \tag{32}\]  
Figure 4: Schematic diagram of the ELUM method. where \(LC_{ij}\) represents the consistency evaluation result of the pixel at coordinate \((i,j)\) and the signal components of the surrounding eight neighborhood regions. \(G_{ij}\) coordinates \((i,j)\) as the center of the 3 \(\times\) 3 area. \(G_{ij}^{k}\) corresponds to the first number \(k\), a neighborhood grayscale average. The value of \(k\) is eight. The component consistency evaluation \(LC_{ij}\) shows the following results:  
* If the location of the \(G_{ij}\) region center is in high consistency with its eight neighboring regions, then \(LC_{ij}\approx 1\);
* If the energy at the center of the \(G_{ij}\) region is low, then \(LC_{ij}<1\);
* If the energy in the center of the \(G_{ij}\) region is higher, \(LC_{ij}>1\). In information theory, entropy is usually used to represent the uncertainty of random variables; that is, to calculate the expected amount of information, the following equation is used:  
\[H(X)=-\sum_{x\in X}p(x)\times\log p(x) \tag{33}\]  
where \(p(x)\) is the occurrence probability of the event \(x\). In evidence theory, the confidence assignment function is often used to assign \(p(x)\). Based on this, a local component uncertainty method based on a variation entropy operator is proposed, which uses local consistency as the confidence assignment function. When the window is crossed over the target region, the component uncertainty in the region is high because the local component consistency is low and the consistency confidence assignment function is low. The uncertainty of the component consistency of the local spatial signal can be measured by the variation entropy operator. The proposed mutation entropy operator is expressed as follows:  
\[U_{ij}=-\sum_{k=0}^{K}M_{ij}^{k}\times\log\biggl{(}1-\left(M_{ij}^{k}\right) ^{2}\biggr{)} \tag{34}\]  
where \(U_{ij}\) is the uncertainty of the position of the pixel \((i,j)\).