# Joint SAR Image Time Series and PSInSAR Data Analytics: An LDA Based Approach
## 4 Experimental Setup
### Preprocessing  
The image preprocessing step consists mainly of the compensation of different acquisition geometries. Each image is acquired from a different position of the satellite, therefore, in each dataset, the slave acquisitions need to be resampled into the geometry of the reference image. This step is called co-registration and is usually implemented at subpixel level. Distances between the satellites' orbits during dataset image acquisition are called perpendicular baselines. This preprocessing step is conducted using the interferometric processing software Gamma RS [24]. Its implementation will be performed differently for the two datasets, due to their different acquisition modes. An oversampling factor equal to 4 will be adopted in both cases, to implement the images alignment at subpixel level. Oversampling is conducted in the spectral domain. The execution of this step is more straightforward in the case of the ERS dataset. Spatial offsets between each master-slave image pair are estimated by maximization of the amplitude's cross-correlation \(R_{A}\), which is computed in multiple sliding windows \(L\) defined across the test region:  
\[R_{A}=\frac{\sum\limits_{l\in L}A_{ml}A_{sl}}{\sqrt{\sum\limits_{l\in L}A_{ml}^ {2}\sum\limits_{l\in L}A_{sl}^{2}}} \tag{8}\]  
where \(A_{m}\) and \(A_{s}\) represent the amplitude values form the master and slave images. By maximization of Equation (8) variable offsets are estimated across the scene in both range and azimuth directions. Those offsets form the basis for determination of resampling polynomials, which are used to convert the slave images to master acquisition's geometry. In this case, the co-registration process can be directly implemented on the test region, presented in Figure 4-A. Validation process is conducted by computation of the amplitude's correlation index of each co-registered master-slave image pair. Spatial variation of the mean value of this parameter, in case of ERS dataset, is shown in Figure 5. The mean value of the amplitude's correlation index distribution is presented here as equal to 0.33. Peak values of this parameter are present in urban regions, reaching values above 0.9. Considering that those values are close to unity, co-registration process of ERS dataset's images is validated. The co-registration process is more delicate in the case of the Sentinel-1 dataset. In TOPS acquisition mode, multiple swaths of the scene are simultaneously illuminated by switching the antenna between consecutive bursts. Focused images of the dataset consist of three swaths, each swath containing nine bursts. Regions covered within consecutive bursts slightly overlap at their  
Figure 4: Amplitude of European Remote Sensing (ERS) dataset’s master image, Buzău region. Acquisition date: 11 August 1997 (**A**). Amplitude of Sentinel-1 dataset’s master image, Constanta region. Acquisition date: 20 November 2015 (**B**). boundaries. During illumination of each burst, the antenna beam is electronically steered in the azimuth direction. The main feature of this acquisition mode is the increased scene coverage. It is similar to the ScanSAR approach, but has the advantage of a constant SNR in the azimuth direction, across the illuminated scene. The antenna's steering during scene illumination induces a Doppler frequency variation across each burst, in the azimuth direction. If the image alignment is not precise, Doppler frequency shifts from bursts borders will affect further interferometric processing of the dataset, including the PS detection step based on spectral analysis. An advantage of this dataset is that orbit related information is accurate in the case of the Sentinel-1 satellite constellation. A coarse co-registration step can be implemented by estimating a set of constant offset values in both range and azimuth directions based on orbit trajectories. This step was not conducted on the previous dataset because orbit state vectors are not reliable in case of ERS constellation.