# A CSAR 3D Imaging Method Suitable for Edge Computation
## 3 A CSAR 3D Imaging Method Suitable for Edge Computation
### Algorithm Complexity Analysis  
The traditional 3D BP imaging algorithm has to perform phase compensation for each 3D grid in each azimuth pulse, so the imaging speed is extremely low. In this paper, IRT and Hough transforms are used to extract the 3D point cloud, which can greatly improve the rate of CSAR 3D imaging. Let the azimuth pulse number of the full CSAR aperture data be \(N_{a}\), the distance pulse number be \(N_{r}\), and the 3D imaging grid size be \(N_{x}\times N_{y}\times N_{z}\).  
The traditional 3D BP algorithm needs \(N_{x}\times N_{y}\times N_{z}\times N_{a}\) phase compensation operations, and the algorithm time is as follows:  
\[T_{\text{BP}}=N_{x}\times N_{y}\times N_{z}\times N_{a}\times t_{1} \tag{18}\]  
where \(t_{1}\) is the time consumption of one phase compensation operation using the traditional 3D BP algorithm.  
The BP 3D imaging method requires one geometric interpolation kernel construction, \(M\times N_{a}\) interpolation and phase compensation operations, and \(N_{x}\times N_{y}\times N_{z}\times N_{a}\) vector search operations. The algorithm time is as follows:  
\[T_{\text{IBP}}=M\times N_{a}\times t_{1}+t_{2}+N_{x}\times N_{y}\times N_{z} \times N_{a}\times t_{3} \tag{19}\]  
where \(t_{2}\) denotes the time consumption of one geometric interpolation kernel construction, and \(t_{3}\) denotes the time consumption of one vector search operation.  
The proposed method needs to extract the ridge line of the sinusoidal trajectory once, including an \(N_{r}\times N_{a}\) prediction of Climber movement. For \(N_{z}\) IRT sub-aperture fusion imaging, if the full aperture data are divided into \(N^{\prime}\) sub-apertures, each imaging dataset includes \(N^{\prime}\) IRT and one sub-aperture image fusion based on GLRT; then, \(N_{x}+N_{y}\) Hough transforms are used to extract the intersection points with one vote for fusion. The time consumption is as follows:  
\[T_{\text{IDI}}=N_{r}\times N_{a}\times t_{4}+N_{z}\times\left(N^{\prime}\times t _{51}+t_{52}\right)+\left(N_{x}+N_{y}\right)\times t_{61}+t_{62} \tag{20}\]  
Figure 4: Schematic diagram of extracting a 3D point cloud via Hough transform; (**a**) layering along the X (Y) direction; (**b**) Hough transform output intersection point; and (**c**) voting fusion of the intersecting points.  
where \(t_{4}\) is the time consumption of one Climber motion prediction, \(t_{51}\) indicates the time consumption of one IRT, \(t_{52}\) is the time consumption of one sub-aperture image fusion based on GLRT, \(t_{61}\) indicates the time consumption of one Hough transform to extract intersection points, and \(t_{62}\) is the time consumption of one vote for fusion.  
The proposed algorithm simplifies the \(N_{x}\times N_{y}\times N_{z}\times N_{a}\) phase compensation operation of the traditional 3D BP or IBP algorithm into \(N_{r}\times N_{a}\) Climber motion prediction, \(N_{z}\times N^{\prime}\) IRT, \(N_{z}\) sub-aperture image fusion, \(N_{x}+N_{y}\) Hough transform to extract the intersection points, and one voting fusion, which effectively simplifies the computational complexity of the model and improves the imaging speed.