## 3 Methodology
### Target-Oriented Processing Module  
In this subsection, we introduce the second module in our proposed imaging framework, the target-oriented processing module. From the perspective of software resource consumption, this module is designed to reduce the consumption of computation time. In general, the resource consumption of computation time is mainly determined by time and spatial complexities. To reduce them, we first reduce the data amount to be processed, by means of target-oriented processing that only handles the echoes from targets; secondly, we execute the computation process in a parallel streaming way through a GPU device. First, as depicted in Formula (8), the received echoes from a target consist of multiple single-frequency signals. Their frequencies are linearly related to the range distance of the points. Thus, imaging in the range direction is conducted through IFFT, which can be expressed as  
\[s_{r}(t,\eta,i)=\sum_{l=1}^{N_{T}}A_{l}sinc[K_{r}T_{r}(t-t_{0l}(\eta))]\exp\{- /2\pi f_{0}t_{0l}(\eta)\} \tag{14}\]  
We can see from the result that multiple \(sinc\) function peaks exist, and their peak locations correspond to the positions of the target points. The mainlobe width of these \(sinc\) functions is inversely proportional to the transmitting signal bandwidth. In other words, through dechirping receiving and IFFT processing, the resolution of the imaging result in the range direction is the same as the current match-filtering processing. The designed process contains one multiplication operation and one fast Fourier transform (FFT) operation. As for the matched-filtering way, it includes one operation of FFT to transform echoes in the time domain into the frequency domain, one multiplication operation with the matched filter, and one operation of IFFT to transform it back into the time domain. Thus, the designed processing saves one operation of FFT. Second, as depicted in (14), one phase term that contains the range histories exists. For imaging in the azimuth direction, this phase term needs to be compensated via parallel streaming BP. As presented earlier in the last subsection, we use the GPU device to conduct streaming BP, which means that one range imaging result is obtained in one azimuth moment; it is streamed into one column of aperture buffer after interpolation via zero \begin{table}
\begin{tabular}{c c c c} \hline
**Item** & **The Current One** & **The Proposed One** & **Relative Reduced Proportion \({}^{*}\)** \\ \hline Sampling frequency (range) & \(c_{1}B_{r}\) & \(\alpha_{1}(c_{1}B_{r})\) & \(\alpha_{1}\ll\mathbf{1}\) \\ Storage occupation (range) & \(c_{1}c_{2}B_{r}W_{rs}\) & \(\alpha_{1}\alpha_{2}(c_{1}c_{2}B_{r}W_{rs})\) & \(\alpha_{1}\alpha_{2}\ll\mathbf{1}\) \\ Storage occupation (azimuth) & \(c_{3}(\text{PRF-}W_{ss})\) & \(\beta(c_{3}\text{PRF-}W_{ss})\) & \(\beta\ll\mathbf{1}\) \\ \hline \end{tabular}  
* 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, the total number is still rather small, as shown in Figure 4. Hence, the relative reduced proportion is just slightly changed and still applied to some extent.  
\end{table} 
Table 1: Resource consumption of the proposed receiving module. padding in the frequency domain. Following this step, every thread corresponding to every pixel in the 2D image traces the corresponding position of response in the aperture buffer at this moment, and takes it out with the phase compensation term to coherently accumulate. Once the necessary resolution is obtained, the image buffer streams out the current 2D imaging result to the massive storage device, as shown in Figure 9.  
Specifically, every thread's calculation includes steps as follows. 1. Calculate the time delay in the range direction.