**5. Results**

### *5.1. Results on the Simulation Data*

After obtaining the trained network, in the testing stage, a noisy interferogram with a coherence coefficient of 0.5 shown in Figure 6b from the simulated testing sets was used to qualitatively assess the performance of the proposed method in this article. Figure 6a is the corresponding reference interferogram. In order to validate the proposed method, we compared it with the Lee filter [18], Goldstein filter [26], InSAR-BM3D filter [28], traditional ISTA algorithm [43], Phi-Net [31], and PFNet [30]. All filtered results are illustrated in Figure 7. Figure 7(a1–g1) represents the filtered interferograms of the seven approaches, respectively. Qualitative evaluation with the naked eye showed that the result of the proposed method was closest to the ideal interferogram shown in Figure 6a. We calculated the difference phases of the seven filtered results and the corresponding ideal interferogram, respectively, and show the difference images in Figure 7(a2–g2). From Figure 7(a2–g2), we can see that the difference image of the proposed method was closest to zero, which further verified that the filtered result obtained by the proposed method was most similar to the ideal interferogram. Moreover, the SSIM maps shown in Figure 7(a3–g3) were computed to assess the capability of the phase detail preservation, where it can be seen that the SSIM

map of the proposed method (Figure 7(g3)) had the most regions whose values were close to 1 amongs<sup>t</sup> all of the testing methods. The above preliminary comprehensive qualitative analysis showed that the proposed method had the best visual performance in both the suppression noise and phase edge detail preservation.

**Figure 6.** A simulated testing interferogram patch: (**a**) Clean interferogram patch; (**b**) noisy interferogram patch with a coherence coefficient of 0.5.

The qualitative evaluation is too subjective and unstable, and testing only a noisy interferogram is haphazard. Therefore, we calculated the mean MSE and MSSIM of all results obtained by the experiments on all of the testing sets with the same coherence coefficients, and these results are shown in Figure 8. In Figure 8, we can intuitively see that the MSE of the proposed method was lower and the MSSIM was higher than the six reference methods. This demonstrates that the proposed method has the characteristics of the best noise suppression and phase detail feature preservation capabilities among the seven methods.

Finally, the mean values of all metrics are presented in Table 1. In Table 1, the proposed method had the highest MSSIM, lowest MSE, and NOR among the seven methods. Through a comprehensive comparison, the performance of the proposed method was optimal among the seven methods. In detail, the NORs of the proposed method, InSAR-BM3D, Phi-Net, and PFNet were equal to 0, which demonstrates that the denoising ability of the four methods is powerful. However, the proposed method could better balance between the noise reduction and phase edge feature preservation because it had the highest MSSIM and the lowest MSE. Furthermore, the running time (T) of the proposed method was the shortest. Compared to Phi-Net and PFNet, the mean T of the proposed method was 87.2% and 85.5% faster, respectively. This means that the proposed method had the most powerful computational capability among the seven methods.

**Figure 7.** *Cont*.

**Figure 7.** The analysis of the simulated interferogram patch: (**a1**–**g1**) Filtered interferograms of the Lee filter, Goldstein filter, InSAR-BM3D filter, ISTA, Phi-Net, PFNet, and the proposed method; (**a2**–**g2**) difference images of Figure 6a and (**a1**–**g1**) in sequence; (**a3**–**g3**) SSIM maps of Figure 6a and (**a1**–**g1**), respectively.

**Table 1.** The metrics of the seven methods on the simulated interferogram. MSSIM is the core accuracy index. T is the speed index.


**Figure 8.** The metrics of the seven methods on the simulated interferograms with ten coherence coefficients: (**a**) mean MSE; (**b**) mean MSSIM.

### *5.2. Results on the Real Data*

In order to validate the performance of the proposed method in real data, we employed two measured interferograms with the size of 512 × 512 pixels to perform the test experiments. As shown in Figure 9, these were provided by the Sentinel-1 SAR satellite. In order to prove the filtering performance of the proposed method in different shapes and different coherence areas, Figure 9a,b shows a high-coherence area A with a dense fringe and low-coherence area B with flatness, respectively.

**Figure 9.** The measured interferograms: (**a**) Area A with high coherence; (**b**) area B with low coherence.

The seven methods were used in area A, as shown in Figure 9a and the results are shown in Figure 10a–g, respectively. From the perspective of vision, the proposed method has a more powerful noise reduction capacity than the Lee filter, Goldstein filter, InSAR-BM3D filter, and traditional ISTA. Compared to Phi-Net and PFNet, their denoising abilities were comparable, but it can be seen from the black rectangles in Figure 10e–g that the phase detail feature preservation ability of the proposed method was stronger.

**Figure 10.** The filtering results obtained by processing Figure 9a using the seven methods: (**a**) filtering interferogram of the Lee filter; (**b**) filtering interferogram of the Goldstein filter; (**c**) filtering interferogram of the InSAR-BM3D filter; (**d**) the filtering interferogram of ISTA; (**e**) the filtering interferogram of Phi-Net; (**f**) the filtering interferogram of PFNet; (**g**) the filtering interferogram of the proposed method.

Next, we computed the number of residues (NOR), the no-reference metric Q, and the running time (T), listed in Table 2, to assess the performance of the proposed method more accurately. From Table 2, it can be seen that the NOR of the proposed method was lower than that of the Lee filter, Goldstein filter, InSAR-BM3D filter, and ISTA algorithm, and its metric Q was higher than that of the four methods. This strongly proves that our method was superior to the four reference methods in both the noise suppression and preservation of edge detail. Furthermore, compared with the Phi-Net and PFNet, the NOR of the proposed method was higher, but its metric Q was 9.9% and 7.8% higher, respectively, which demonstrates that the proposed method was superior to the Phi-Net and PFNet in the phase edge detail preservation (i.e., it provided a well-balanced noise reduction and fringe detail preservation). From the perspective of processing efficiency, the running time of the proposed method was the shortest with only 1.43 s among the seven methods and was 51.9% faster than the PFNet. In conclusion, the proposed method performed better than the six reference approaches in both the filtering performance and speed.

**Table 2.** The metrics of the seven methods on the measured interferogram of area A. Metric Q is the core accuracy index. T is the speed index.


Area A is a high-coherence area with dense fringe. Therefore, in order to prove the adaptability of the proposed method to different terrain regions with different levels of noise, we selected a flat area (area B shown in Figure 9b) of low coherence to experiment further. The filtering results of the seven methods are shown in Figure 11a–g. From Figure 11a–g, we can see that our method offers the best-balanced noise suppression and the preservation of the phase edge texture. In more detail, the denoising ability of the proposed method was obviously stronger than the three widely-used methods. The traditional ISTA algorithm lacks a denoising ability, but also suffers from a serious loss of phase details. As shown in the black rectangles in Figure 11e–g, compared with the Phi-Net and PFNet, it was obvious that the proposed method preserved the phase detail features more completely, while the PFNet filtering excessively resulted in a serious loss of phase details. Similarly, the indicators of all of the results obtained by the seven methods were calculated for a quantitative assessment and are listed in Table 3. The performance of the proposed method was obviously better than that of the three widely-used methods, the ISTA algorithm and Phi-Net. Then, the proposed method has a 19.8% higher metric Q compared with PFNet. Combined with the quantitative indexes of area A and area B as shown in Tables 2 and 3, we can see that the performance reduction in the PFNet was significantly higher than that of the proposed method. This proves that the proposed method had better generalization.


**Table 3.** The metrics of the seven methods on the measured interferogram of area B. Metric Q is the core accuracy index. T is the speed index.
