# A CSAR 3D Imaging Method Suitable for Edge Computation
## 3 A CSAR 3D Imaging Method Suitable for Edge Computation
### Algorithm Flow  
A flow chart of the CSAR fast 3D imaging method based on image detection presented in this paper is shown in Figure 2. This method includes three steps: (1) using the Crazy Climber algorithm to extract the sine track ridge [15], (2) using IRT to obtain the CSAR height profile, and (3) applying Hough transform to extract a CSAR 3D point cloud. The details are as follows. Figure 2: Flowchart of the proposed method. **Step 1**: Extract the sine track ridge. Because the sinusoidal trajectories of different targets overlap and cross in the range-compressed echo signal, high-quality CSAR images cannot be obtained directly by IRT. The improved Crazy Climber algorithm is used to extract the spine of the target sinusoidal trajectory [15], which can effectively improve the imaging effect of CSAR. The specific steps of the improved Crazy Climber algorithm are as follows. (1) Initialization. \(s_{\mathrm{r}}(\tau,\varphi)\) is the \(M\times N\) observation matrix, the observation matrix \(R\) and the measurement matrix \(D\) are zero matrices with the exact dimensions of \(s_{\mathrm{r}}(\tau,\varphi)\), and the \(K\) Climbers are evenly distributed in the observation matrix \(R\). Let the number of climber moves be \(n\). (2) Move the Climber. The time corresponding to the movement of the Climber is \(t_{k}(k=1,2,\cdots,n)\). If the position of the Climber at time \(t_{\mathrm{k}}\) is \(pos(t_{k})=(i,j)\), the rule for estimating the position of the Climber \(pos(t_{k+1})=(i^{\prime},j^{\prime})\) at time \(t_{\mathrm{k+1}}\) involves calculating the probability of the Climber moving to the adjacent six positions:  
\[p_{u}=\frac{\Delta A^{\prime}{}_{u}}{\sum\limits_{u=1}^{6}\Delta A^{\prime}{} _{u}} \tag{15}\]  
where \(\Delta A^{\prime}{}_{u}=S(A_{u})-S(pos(t_{k}))+|\min(S(A_{u}))-S(pos(t_{k}))|\), and \(S(A_{u})-S(pos(t_{k}))\) is the amplitude increment of the six adjacent positions \(A_{u}(u=1,2,\cdots,6)\) relative to the position \(pos(t_{k})\). When \(pos(t_{k})\) is located inside the matrix, that is \(2\leq i\leq M-1\) and \(2\leq j\leq N-1\), the adjacent six positions are \(A_{1}(i-1,j-1)\), \(A_{2}(i,j-1)\), \(A_{3}(i+1,j-1)\), \(A_{4}(i-1,j+1)\), \(A_{5}(i,j+1)\), and \(A_{6}(i+1,j+1)\). Conversely, when \(pos(t_{k})\) is located at the edge of the matrix, first connect the end of the matrix \(s_{\mathrm{r}}(\tau,\varphi)\) and then shift it. For example, if \(i=M\) and \(2\leq j\leq N-1\), the adjacent six positions are \(A_{1}(i-1,j-1)\), \(A_{2}(i,j-1)\), \(A_{3}(1,j-1)\), \(A_{4}(i-1,j+1)\), \(A_{5}(i,j+1)\), and \(A_{6}(1,j+1)\), as shown in Figure 3.  
(3) According to the moving result, add 1 to the corresponding position of the measurement matrix \(D\). (4) Repeat the above steps until the Climber traverses \(s_{\mathrm{r}}(\tau,\varphi)\) to obtain the final metric matrix \(D\). (5) Recurse the measurement matrix \(D\) in the slow time direction to form a sinusoidal ridge line \(s_{\mathrm{r}}(\tau,\varphi)\) and eliminate the ridge lines with too small a length to obtain the ridge line matrix \(s_{\mathrm{r}j}(\tau,\varphi)\). **Step 2**: Obtain the CSAR height profile. Two-dimensional profiles of CSAR with different heights are obtained via IRT. (1) Divide the sub-apertures. According to the scattering characteristics of the target in the scene, \(s_{\mathrm{\eta}}(\tau,\varphi)\) is divided into sub-apertures \(s_{\mathrm{rj\_sub,i}}(\tau,\varphi)\) along the slow time, where \(i=1,2,\cdots,N^{\prime}\), \(N^{\prime}=\frac{N}{B_{\mathrm{sub}}}\) is the number of sub-apertures, and \(B_{\mathrm{sub}}\) is the sub-aperture width;  
(2) Set the height of the imaging plane \(h_{k}(k=1,2,\cdots,K)\). By changing the range center of the data \(s_{\mathrm{rj\_sub,i}}(\tau,\varphi)\) during the IRT, 2D imaging of the CSAR at different height planes can be realized;  
(3) Sub-aperture IRT imaging.