# FDBP-InSAR: An Efficient Algorithm for InSAR Imaging via Frequency Domain Back Projection
## 3 InSAR Imaging via FDBPA
### Algorithm Flow
The COH of interferogram in Figure 6a-c is 0.812, 0.802, and 0.809, respectively, which demonstrates the phase-preserving ability of the proposed algorithm is better than the traditional frequency-domain algorithm. InSAR algorithm based on TDBP, RD, and FDBP spent 8805.7, 37.28, and 1102.40 s, respectively, to process the airport echo data with the GPU. It shows that the proposed algorithm improves imaging efficiency, compared with TDBPA. ## 5 Performance Analysis

### The Number of Frequency Grids

FDBPA applies back-projection ideal to the range frequency domain. Grid division is the most important step in the frequency back-projection algorithm. Different from the grid division of the time-domain back-projection algorithm, the range of the frequency-domain grid is a fixed value \(2\pi\). Therefore, the interval of frequency grids and the number of frequency grids become important indexes

Figure 6: InSAR imaging results of the airborne large scene. (**a**) TDBP, coherence (COH): 0.812, time: 8805.70 s; (**b**) RD, COH: 0.802, time: 37.28 s; and (**c**) FDBP, COH: 0.809, time: 1102.4 s (top: amplitude, and bottom: interferogram). to determine the imaging accuracy of FDBPA. To further explore the imaging characteristics of FDBPA, we will test the influence of these two parameters on the proposed algorithm one by one. For testing the impact of the number of frequency grids on FDBPA, fixing the interval of grids, FDBPA with different numbers of grids are implemented to obtain the amplitude images and interferograms from the raw echo data of the simulation cone. The simulation system parameters are the same as the simulation parameters in the fourth part. The qualities of imaging results are measured by entropy, residue, coherence, absolute phase difference, and so on. Figure 7 shows simulation results of FDBPA with the number of grid points of \(1000\,\times\,1000\), \(2000\,\times\,2000\), \(4000\,\times\,4000\), and \(6000\,\times\,6000\), respectively. Obviously, details of the cone scene in the amplitude images of Figure 7a-c are well restored, and interferometric fringes of interferograms are clear and consistent. There are similar and the change is not obvious. However, as shown in Figure 7d, the focused image is blurred seriously and the interferometric fringes become indistinct. It demonstrates when the interval of grids fixed, with the increase of grids, the scope of the spectrum search is expanded. When the scope reaches a certain level, zero-frequency information will be obtained in the echo data, causing the original scene information covered. According to (17), (18), and (19), the value of sharpness, residue, and the absolute phase difference is related to the number of frequency grids. For eliminating the impact of the change of the number of frequency grids on image evaluation indicators, 2D interpolation is carried out to fix all the focused images size to \(6000\,\times\,6000\). Figure 8 shows the changing trend of ENT and RES of the focusing results. Figure 8: Quality index of simulation data. Figure 7: The results of the simulated cone: (**a**) \(1000\,\times\,1000\), (**b**) \(2000\,\times\,2000\), (**c**) \(4000\,\times\,4000\), and (**d**) \(6000\,\times\,6000\). (Top: amplitude. Bottom: interferogram.). ### The Interval of Grids

To observe the influence of the grid interval on the proposed algorithm, simulations under different intervals of grids are carried out. The remaining simulation parameters are consistent with that in the fourth section. Fixing the number of grids and observing the imaging characteristics of FDBPA with the grid interval of 0.5, 0.75, and 1.5 \(K\), respectively, where \(K=2\pi/W\), and \(W\) is the imaging scene range. According to the time-frequency-domain transformation principle, the increase of frequency interval leads to the decrease of interval in the time domain, which results in a reduction in the size of the focused images.