# Application and Evaluation of the Gaofen-3 Satellite on a Terrain Survey with InSAR Technology
## 3 Interferometric Data Processing
### Phase Filtering  
In this study, the multi-scale phase-filtering method in the wavelet domain was used to conduct phase filtering on the flattened interferogram. This method was compared with the classical Lee and the improved Goldstein filter methods [21; 22] to validate the ability of phase noise removal and preserve the phase details and edges. It has been proved to have better filtering precision and can reduce the influence of data processing errors on the evaluation experiment. The multi-scale phase filtering method based on the wavelet domain is shown in Figure 6. The filtering algorithm was based on the analysis of the wavelet residual band using discrete digital transformations, which consisted of six steps described briefly below. The details are described by [PERSON] and [PERSON] [23]. Figure 5: Interferograms of the Sentinel-1 satellite data in the Dengfeng area, China: (**a**) interferogram with temporal baseline of six days, (**b**) interferogram with temporal baseline of thirty-six days, (**c**) coherence map of the interferogram with temporal baseline of six days, (**d**) coherence map of the interferogram with temporal baseline of thirty-six days. Step 1: three-level wavelet transform on the complex interferometric phase. In the third decomposition level, the wavelet filter was applied to all bands using a discrete wavelet package transform (DWPT). Step 2: mask generation. The pixel of the mask was determined by the signal quality. Step 3: Real and imaginary parts. The real and imaginary parts of the coefficient detected as the signal were multiplied by 2, and the noise coefficient remained unchanged. Step 4: inverse discrete wavelet transformation. Only one wavelet scale was reduced. Step 5: mask-locating signal coefficients. To obtain mask-locating signal coefficients for previous scales (higher-frequency scales), a new mask was derived from that generated in step 2.) We iterated steps 3-5 (dashed lines in Figure 6) three times to obtain the complex signal in the original domain. Step 6: Phase calculation. Meanwhile, the classical [PERSON] method [22] and the improved [PERSON] method [21] were used to carry out phase filtering and compared to the wavelet-based multi-scale method. Figure 7 is a partial region of the phase image. The original interferometric phase image was annihilated by speckle noise. After processing with the three filtering methods, the SNR of the phase image was improved to different degrees. From the visual effects, the filtering results of the Lee method kept a certain proportion of phase noise, whereas the [PERSON] method and our method had almost the same effect on noise removal. It was visually judged that both the Goldstein and our method outperformed the Lee method with regards to phase de-noising ability. Therefore, the Goldstein method was mainly used as a comparison to our method; the Goldstein method retained a small amount of noise signal, and some effective signal components were lost to a certain extent. However, for the phase image obtained by  
Figure 6: Multi-scale phase filtering process in the wavelet domain via six steps. DWPT: discrete wavelet package transform; DWT: discrete wavelet transform; Imag part: imaginary part; \(\phi_{\mathrm{x}}\): original phase; \(i\): iteration times. our filtering method, the noise level was slightly lower than that of the Goldstein method, and more details and edges were preserved. Figure 8 shows the local details of Figure 7. It can be observed that the [PERSON] method had some ability for maintaining phase details and stripe edges, but the higher noise level still affected the extraction of true phases. On the other hand, the [PERSON] method achieved good results in general, but for some regions, the details were blurred because of the filtering, and even the edges of the phase jump were filtered with poor preservation, which will have a negative impact on the subsequent unwrapping and the inversion of terrain or deformation.