# FDBP-InSAR: An Efficient Algorithm for InSAR Imaging via Frequency Domain Back Projection
## 3 InSAR Imaging via FDBPA
### Algorithm Flow
Patently, the interferometric image of RDA has more noise points and TDBPA and FDBPA have a similar interferometric effect. Meanwhile, the interferometric image of FFBPA looks brightest and clearest because FFBPA based on sub-aperture imaging has a filtering effect on the echo data that reduces the noise points in the interference graph phase. Table 4 shows the quality indicators of Figure 4. The quality indexes of TDBPA and FDBPA are very close compared with the other two algorithms, and FDBPA performs slightly worse than TDBPA within a reasonable range which probably because of environmental noise. Furthermore, It demonstrates that the FDBPA and TDBPA have a better focusing accuracy and property of phase-preserving than RDA and FFBPA. Experiment results further prove that in practical application, FDBPA is an effective InSAR imaging algorithm. It can achieve similar imaging accuracy and the property of phase-preserving with TDBPA. Figure 4: The results of the experiment: (**a**) RD, (**b**) FFBP, (**c**) TDBP, and (**d**) FDBP (top: amplitude, middle: interferogram, and bottom: coherence-map). Figure 5 shows the results of InSAR imaging with a farmland scene. The measured data of this experiment were obtained from an airborne InSAR system based on the operation mode of single send and double receive. The main system parameters of InSAR are as follows: the carrier frequency, \(f_{c}~{}=~{}35\,\mathrm{GHz}\); the signal bandwidth, \(B_{r}~{}=~{}900\,\mathrm{MHz}\); the sampling frequency, \(f_{s}~{}=~{}1\,\mathrm{GHz}\); the antenna aperture length, \(D~{}=~{}0.2\,\mathrm{m}\); the pulse repetition frequency, \(PRF~{}=~{}2500\); the platform height, \(H~{}=~{}1020\,\mathrm{m}\); the radar incident angle, \(\theta~{}=~{}30\,\mathrm{\SIUnitSymbolDegree}\); the baseline length, \(B~{}=~{}3\,\mathrm{m}\); and the reference distance, \(R0~{}=~{}5000\,\mathrm{m}\). This experiment selects part of raw scene data that can reflect the imaging effect to be processed by TDBPA, FDBPA, and RDA, respectively. Table 5 shows the comparison of indicators. It is clear that the imaging efficiency of FDBP is better than TDBPA, while the imaging accuracy and the phase precision are better than TDBP algorithm when processing the same data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Indicator** & **RD** & **FFBP** & **TDBP** & **FDBP** \\ \hline Entropy & 1.2373 & 1.3467 & 1.1820 & 1.1943 \\ Sharpness & 496.90 & 582.95 & 587.36 & 589.76 \\ Residue & \(4.4\times 10^{6}\) & \(2.7\times 10^{6}\) & \(3.1\times 10^{6}\) & \(3.2\times 10^{6}\) \\ coherence & 0.7878 & 0.8045 & 0.8183 & 0.8116 \\ SNR & 0.4406 & 0.4458 & 0.4500 & 0.4480 \\ SPD & \(1.61\times 10^{7}\) & \(1.11\times 10^{7}\) & \(1.20\times 10^{7}\) & \(1.25\times 10^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of quality imaging results. Figure 5: The results of the experiment: (**a**) TDBP, (**b**) RD, and (**c**) FDBP (top: amplitude, and bottom: interferogram). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicator** & **TDBP** & **RD** & **FDBP** \\ \hline Entropy & 1.9202 & 1.8289 & 1.8927 \\ Residue & \(4.0\times 10^{5}\) & \(12.0\times 10^{5}\) & \(5.0\times 10^{5}\) \\ SPD & \(1.42\times 10^{6}\) & \(4.17\times 10^{6}\) & \(1.83\times 10^{6}\) \\ Time(s) & \(1616.8\) & \(11.1\) & \(397.7\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of quality imaging results. Figure 6 shows the results of airborne InSAR imaging with a large scene. The radar system work in Ka-band and \(f_{\rm c}~{}=~{}37\,\)GHz. The ideal imaging resolution is \(0.5\times 0.5\), the signal bandwidth \(B_{r}~{}=~{}300\,\)MHz, the imaging scene size is \(4096\times 3400\). The partial imaging details are shown in the highlighted red wireframe. Patently, the amplitude images of InSAR imaging algorithm based TDBP shows the best imaging effect, the amplitude image of RD-based InSAR imaging has obvious defocusing as shown in Figure 6b, while the amplitude image of InSAR imaging algorithm based FDBP shows a similar imaging effect with TDBP.