## 5 Satellite Remote Sensing Techniques for Infrastructure Monitoring
### Persistent Scatterer Interferometry  
The most conventional MT-InSAR methods are the PS-InSAR, proposed in [14; 15], and the SBAS processing algorithm [16] (Figure 6). Following these pioneering research works, a variety of advanced algorithms were proposed in the past two decades, including the Stanford method for persistent scatterers developed by [PERSON] [68], the stable points network [69], PS Pairs (PSPs) [70], SqueezeSAR [71], quasi-PSs (QPSs) [72], and SAR tomography (TomoSAR) [73]. These methods differ in terms of parameters and processing steps, including their baseline configuration, methods for the selection of persistent scatterers, phase unwrapping strategies, and deformation models (i.e., linear and non-linear). Despite the different terminology associated with these techniques, their main aim and processing strategies are similar. Numerous SAR images, referred to as the stack of data or dataset, are required and must be co-registered to a common grid. Therefore, the interferograms are computed from the stack of the images, which are then flattened using a digital elevation model (DEM) to compute the \"differential\" phase. As a result, the topographic phase term is subtracted and the differential interferograms can be computed. The detection of persistent scatterer candidates (PSCs) relies on three main methods, based on the evaluation of the amplitude dispersion index \(D_{a}\), the phase stability and the correlation methods that depend on the stability values of the phase and the coherence of PSs in the dataset, respectively. The first method based on \(D_{a}\) was proposed by [PERSON] et al. [14; 15] and used to detect the PSs according to the analysis of the amplitude values of the pixels in the time series. The calibrated amplitude stability is statistically related to the phase stability, implying that if a scatterer has a large amplitude to dominate the resolution cell, the clutter has limited influence on the phase. The amplitude dispersion index \(D_{a}\) can be written as [14; 15]:  
\[D_{a}=\frac{\sigma_{a}}{\mu_{a}} \tag{4}\]  
where \(\sigma_{a}\) and \(\mu_{a}\) are the standard deviation and the mean of the backscattering intensity, respectively. In this method, the phase information is not used for the PSC selection, solving the problem of the phase unwrapping, the noise and the atmospheric contributions. These factors can all affect the phase values and introduce errors. It has advantages in terms of high efficiency, easier implementation and being suitable for detection of individual PS points, all of which are useful in infrastructure monitoring. \(D_{a}\) is calculated on a pixel-by-pixel basis and tested against a threshold. Pixels with a value below the threshold are selected as PSCs. To elaborate, a pixel with \(D_{a}\) values below a pre-set threshold, generally ranging from 0.25 to 0.4, can be selected as a suitable PS candidate [14]. Commonly, a minimum number of 25-30 SAR images is required for the detection of PS points to ensure statistical significance and quality of the PSs information. Methods based on phase stability rely on the fact that a PS is a pixel characterised by a stable backscattered value in terms of images collected at different times. Hence, the phase stability can be considered as a criterion for the selection of the PSs. It can be used for this selection according to the signal-to-clutter ratio (SCR) [74], when the average SCR value of a pixel is higher than an assumed threshold. The SCR can be evaluated as [74; 75]:  
\[r_{sc}=\frac{s^{2}}{c^{2}} \tag{5}\]  
Figure 6: Scheme of the displacement detection by the PSI technique through \(n\) images collected on the same area: \(R_{i}\) is the sensor–to-target distance of the \(i\)th acquisitions, \(\Delta R_{i}\) is the variation with respect to the previous image. where \(s\) is the amplitude and \(c\) is the clutter.