## 3 Methodology
### Decision Module and Feedback Connection  
In this subsection, we introduce the last module in our proposed imaging framework. Moreover, the modules' feedback connections are also introduced, and they are designed to adjust the resource allocation dynamically. As the system's resources are limited, the principle of adjusting is to allocate them as reasonably and adaptive as possible. To allocate them more reasonably, the module adaptively decides the receiving module's receiving window and aperture in the two directions so that resources are spent only on targets. To allocate them more adaptively, the module adaptively decides the necessary resolution of the image. Specifically, the module uses CFAR to extract targets' information, including their position and size. CFAR is a local detector to detect targets with an adaptive threshold [34]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **The Current One** & **The Proposed One** & **Relative Reduced Proportion * \\ \hline Range processing & \(O(N_{rl}logN_{rl})+O(N_{rl}^{\prime})+O(N_{rl}^{\prime})+O(N_{rl}^{\prime})+O( \alpha_{1}\alpha_{2}N_{rl}^{\prime})+O(\alpha_{1}\alpha_{2}N_{rl}^{\prime}log( \alpha_{1}\alpha_{2}N_{rl}^{\prime}))\) & \(\approx\alpha_{1}\alpha_{2}\ll\mathbf{1}\) \\ Azimuth processing & \(O(2N_{a}N_{x}N_{y})\) & \(O(2\alpha_{1}\beta\gamma N_{a}N_{x}N_{y})\) & \(\approx\alpha_{1}\beta\gamma\ll\mathbf{1}\) \\ \hline \hline \end{tabular}  
* We compare the time consumption from the perspective of computation complexity. The above analysis is based on the situation that only one target exists in the scene for simplification. Although more targets exist in the scene in practice, the number is still relatively small, as shown in Figure 4. Hence, the relative reduced proportion is just slightly changed and still applied to some extent.  
\end{table} 
Table 2: Computation time consumption of the proposed processing module *. For a single target's pixel under detection, its surrounding clutter and noise pixels are used to calculate the corresponding threshold as  
\[T=\frac{\rho}{N_{c}}\sum\
olimits_{m=1}^{N_{c}}x_{m} \tag{19}\]  
where \(x_{m}\) is the amplitude of clutter and noise pixel in the image, \(m\) is the pixel index, \(N_{c}\) is the number of pixels, and \(\rho\) is the constant related to false alarm probability. To avoid the miscalculation with the target's pixels being mixed in, guard pixels are set adjacent to the pixel under detection, as shown in Figure 10.  
Meanwhile, the module uses image entropy [19] to decide the necessary resolution in the azimuth resolution. The image entropy is calculated as follows:  
\[ \begin{array}{c}H=\sum\sum\frac{|I(x,y)|^{2}}{S}.ln\frac{S}{|I(x,y)|^{2}}\\ S=\sum\sum|I(x,y)|^{2}\end{array}  \tag{20}\]  
where \(I(x,y)\) is the amplitude of pixel \((x,y)\) in the image. The entropy is to measure the randomness of the image statistically. In the SAR imaging community, it is usually used to indicate the degree of image focusing [19]. Normally, the more the image is focused, the lower the entropy is. In another information theory perspective, entropy indicates the amount of uncertainty. For random parts in the image--the clutter and noise--it has higher entropy than the targets'. When the resolution is low, the entropy difference between the part of targets and the part of the clutter and noise is not significant. As the resolution is increased, the difference increases, which is beneficial for target detection. Initially, the target entropy is decreased rapidly. As target details are gradually revealed, the decreasing rate of entropy becomes low, as shown in Figure 11. Based on this, the module decides that the necessary resolution is achieved when the relative rate of change is lower than a threshold. Finally, we introduce a feedback connection. The proposed receiving, processing, and decision modules are connected through this feedback connection so that the decision module can adapt to other modules' parameters.