# FDBP-InSAR: An Efficient Algorithm for InSAR Imaging via Frequency Domain Back Projection
## 3 InSAR Imaging via FDBPA
### Algorithm Flow
The increase of the scene area leads to the decrease of the interval of grids and the increase of grids, while the number of imaging cells of the target scene in focused images is invariable. It is obvious that the amplitude images and interferograms are consistent with each other and have similar imaging effect under different imaging scene size. Table 8 shows the indicators of the images in Figure 13. The value of these indexes varies in a reasonable range with the increase of scene size. Figure 14 is the experiment results. The amplitude images and interferograms with different imaging scene sizes have similar effects. With the increase of the



## 6 Conclusions

In this paper, we propose an InSAR imaging algorithm based on FDBPA with high-precision focusing and accurate phase-preserving. It applies the idea of back-projection in the frequency domain, to resolve the defocusing problem caused by range migration correction (RMC) of the traditional frequency-domain algorithm. The proposed algorithm introduces the precise antennas and scene-position information obtained from the advanced positioning system and inertial measurement unit in the imaging process. Furthermore, when compensating for the delay phase in the two-dimensional wavenumber domain, we use the real distance information from each field to the antenna, instead of the reference scene distance, which improves the focusing and phase precision and ensures the phase accuracy and stability of the proposed algorithm. The back-projection step in frequency domain avoids the repetitive calculation of the index values of the back-projection in time domain and improves the imaging efficiency on the base of the time-domain InSAR imaging algorithm. Moreover, the larger the imaging scene is, the more obvious the effect will be. Simulation and experiment results in the fourth section primarily verify the feasibility of the proposed algorithm. The InSAR imaging algorithm based on FDBP can achieve imaging and phase accuracy similar to that of the time-domain algorithm, which is much higher than that of the frequency-domain InSAR imaging algorithm. Compared with the time-domain imaging algorithm, the proposed scheme can improve the imaging efficiency by at least three times. As the scene grows larger, its imaging efficiency advantages become more and more obvious. Results in the fifth section demonstrate that with the increase of frequency grids number, the imaging effect goes up and then down, and with the increase of grid interval, the imaging effect goes up and then down. The frequency grid number and grid spacing of the FDBP-based InSAR imaging algorithm can be calculated by the equations in calculation of index of Section 3.2, where the imaging scene size should be the same as the real measured scene size. Figure 14: The results of experiments: (**a**) 1 times, (**b**) 1.5 times, (**c**) 2 times, and (**d**) 2.5 times. (Top: amplitude. Bottom: interferogram.). **Author Contributions:** Conceptualization, Y.W. and S.W. ; methodology, Y.W. and S.W. ; software, [PERSON] and J.L. ; validation, Y.W. and J.L. ; formal analysis, M.W. ; investigation, Y.W. ; resources, S.W. ; data curation, Y.W. ; writing--original draft preparation, Y.W. ; writing--review and editing, Y.W. ; visualization, S.W. ; supervision, X.Z. ; project administration, S.W. ; funding acquisition, S.W. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the National Key R&D Program of China under Grant (2017-YFB0502700), National Natural Science Foundation of China (61501098, 61671113), the China Postdoctoral Science Foundation Funded Project (2015M570778), and the High Resolution Earth Observation Youth Foundation (GFZX04061502). **Conflicts of Interest:** The authors declare no conflict of interest. ## References

* (1) [PERSON]; [PERSON]; [PERSON] (Eds.) _Principles of Synthetic Aperture Radar Imaging_; University of Electronic Science and Technology Press: Chengdu, China, 2007. * (2) [PERSON] Synthetic Aperture Radar. _IEEE Trans.