## 3 Methods
### SAR Dataset Processing  
The pre-processing of the heterogeneous SAR images of Sentinel-1A and GF-3 mainly includes the steps of image alignment, multi-view, filtering, radiation correction, etc. Figure 4 shows the processing of the GF-3 image on 20 July.  
1. Multi-looking processing: The Sentinel-1A SLC image is multi-view processed with a view number ratio of 4 \(\times\) 1, and the GF-3 SLC image is multi-view processed with a view number ratio of 2 \(\times\) 2 to attenuate the influence of coherent speckle noise information on the image quality.
2. SAR image filtering: In this paper, the enhanced Lee filtering method is used for SAR image filtering, which effectively overcomes the shortcomings of the traditional Lee filtering method for non-homogeneous areas with poor filtering effects and adopts the process of distinguishing the target distribution in the image area and divides the SAR image area into the homogeneous area, the non-homogeneous area, and the separation point target area. In this paper, the enhanced Lee filtering method with a  
Figure 4: GF-3 SAR image on 20 July (drawing mode is Square Root). (**a**) Multi-looking. (**b**) Filtering. (**c**) Geocoding and Radiometric Calibration.  
Figure 3: Flow chart of heterogeneous SAR images for road damage monitoring in Zhengzhou City during the “7-20” rainstorm.  
window size of 5 \(\times\) 5 is selected to filter SAR images, which can effectively maintain the edge information of radar images while suppressing noise information.
3. Geocoding and radiometric calibration: Geometric and radiometric corrections are performed to eliminate distortions and obtain the backscatter coefficients of the images by using the 30 m resolution digital elevation data NASA SRTM released.
4. Image registration: By selecting control points on the image, the three SAR images taken before, during, and after the rainstorm are registered and geometrically corrected.  
The SAR system can obtain the power ratio of the measured emission and return pulses, and this ratio (backscattering) is projected to the slant range geometry to better compare SAR images' geometric and radiation characteristics under different SAR sensors and receiving modes. It is necessary to perform geometric and radiation calibration on the slant range SAR data and convert it into a geographic coordinate projection.  
The range of geometric distortion in the SAR image is large, mainly caused by the change in terrain. Based on the given digital elevation model, the relationship between the three-dimensional coordinates of the ground point and the two-dimensional coordinates of the slant distance image is established by the distance-Doppler geometric model and the backward projection algorithm. The range-Doppler model is expressed as [20;21]:  
\[R=S-P \tag{1}\]  
\[f_{D}=\frac{2f_{0}\left(\frac{\
u_{p}-\
u_{b}}{c}\right)R_{s}}{c|R_{s}|} \tag{2}\]  
where \(R_{s}\) is the tilt range, \(S\) and \(P\) are the sensor and backscatter unit positions, \(v_{s}\) and \(v_{p}\) are the sensor and backscatter unit velocities, \(f_{0}\) is the carrier frequency, \(c\) is the speed of light, and \(f_{D}\) is the processed Doppler frequency.  
For better comparison of heterogeneous SAR image data, the radar data need to be radiometrically calibrated using the radar equation to achieve calibration of the radar backscatter coefficient. The radar backscatter coefficient refers to the radar reflectivity per unit area of the target in the incident direction, and the backscatter coefficient can also be regarded as a combination of three elements: unit cross-section, reflectivity, and directionality. The general form of the radar equation is:  
\[P_{r}=\frac{R_{s}A^{2}}{4\pi\lambda^{2}R^{4}}\sigma \tag{3}\]  
where, \(P_{t}\) is the transmitting power of the radar transmitter, \(A\) is the effective scattering transceiver area, \(R\) is the slope distance from the antenna phase center to the target point, \(\lambda\) is the electromagnetic wave wavelength, and \(\sigma\) is the radar scattering cross section.