# SAR Interferogram Filtering of Shearlet Domain Based on Interferometric Phase Statistics
## 4 Validation with Real Data  
### Validation with the Interferogram over the Etna Volcano  
In this section, an interferogram over Mt. Etna Volcano in Italy is selected to verify the proposed filter. The image pairs (Frame: 2853, Track: 222) were acquired on 6 September and 11 October 2000. The vertical baseline is 305 m, the ambiguity height is 31 m, and the intensive fringe area is 400 \(\times\) 400 pixels. The interferometric phase and corresponding coherence map are shown in Figure 7a,b, respectively. Figure 6: Cross-section over the phases filtered by the Goldstein filter, wavelet filter, Lee filter and the proposed filter. The location of the cross-section is shown in Figure 5(a1–d1). Figure 8 shows the filtered results of the Goldstein filter, wavelet filter, Lee filter and the proposed filter. Obviously, these methods have removed the noise and enhanced the edge in high coherence areas. However, a lot of noise in low coherence areas remained in the results of the Goldstein filter and wavelet filter as shown in Figure 8(a1,b1). The Lee filter shown in Figure 8(c1) has filtered out most noises, though it partially damages the edge details in the dense fringe area. The results of the proposed filter shown in Figure 8(d1) keep the main features of the image with clearer and more distinguishable interferometric fringes, especially in low coherence areas. Figure 8: Filtering results of (**a1**) [PERSON] filter; (**b1**) wavelet filter; (**c1**) Lee filter; and (**d1**) the proposed filter; (**a2–d2**) Close-up of results of area A in Figure 7; (**a3–d3**) Close-up of results of area B in Figure 7. (Unit: rad). Figure 7: (**a**) Interferometric phase; and (**b**) corresponding coherence map over Mt Etna Volcano, Italy. A and B, labeled by white rectangles, indicates the enlarged areas. Close-up views of areas A and B in the white rectangles of Figure 7 are shown in Figure 8(a2-d2) and Figure 8(a3-d3), respectively. The average coherence value of area A is high and the coherence of area B is low (Figure 7b). Figure 8(a2) is slightly under-filtered and Figure 8(a3) is slightly over-filtered. The Goldstein filter yields obvious errors and behaves poorly in noise suppression. Compared with the results of the Goldstein method, both the wavelet and Lee methods perform better in noise reduction. In some areas, however, phase noises still exist. The Lee filter is able to retain the details effectively because it adopts the direction filter window. However, as the window has a fixed size, its noise suppression ability is limited in the sparse fringe areas, and it partially damages the edge details in the dense fringe area. The close-up view of the area within areas A and B of Figure 7 from the proposed method is shown in Figure 8(d2,d3). We can see that the proposed methods significantly suppress noise, and interferometric fringes in areas A and B are clearer and more distinguishable. To further analyze the noise reduction and detail preservation, an experiment was conducted. First, we added the deformation phases to the Etna interferometric phase. Second, we used the aforementioned filtering methods to process the phase containing deformation phases. Finally, we obtained the estimated deformation phases using filtering results. The deformation phases were simulated by the peaks function shown in Figure 9a. Estimated deformation phases obtained by the Goldstein, wavelet, Lee and the proposed methods are shown in Figure 9b-e, respectively. In contrast to the real deformation phases, Figure 9 suggests that the Goldstein and wavelet methods show phase difference in almost the whole phase image. The performance of the Lee method is superior to the Goldstein and wavelet methods. However, the proposed method has the best performance among the four methods. Quantitative assessments are listed in Table 2 in terms of the number of residues [34], the phase standard deviation (PSD) [11], the sum of phase difference (SPD) [35] and the root mean square error (RMSE) of the deformation phases.