## 1 Introduction  
Data acquired from synthetic aperture radar (SAR) sensors allows obtaining all-day, all-weather high-resolution complex reflectivity images of large-scale areas. If SAR images are taken at different times, differential SAR interferometry (DInSAR) techniques allow exploiting phase differences, _i.e._, the interferograms, between multi-temporal pairs of single look complex (SLC) images in order to retrieve the displacement information of affected areas [1, 2] with millimetric precision [3]. The exploitation of the interferometric phase is limited by geometrical and temporal decorrelation phenomena [4]. The presence of hard atmospheric artifacts also compromises the applicability of classical DInSAR techniques. In order to overcome these limitations, different persistent scatterer interferometry (PSI) techniques have been developed during the last decade [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. In this case, large datasets of multi-temporal SAR data are employed in order to generate multiple phase relationships, allowing the reliable estimation of both the linear and the non-linear component of terrain displacements, as well as the atmospheric phase screen (APS) for each acquisition. Nowadays, there exist a lot of applications showing their validity for monitoring large-scale deformation episodes, as well as providing a useful technique for their geophysical interpretation. Examples of such applications include, among others, modeling surface deformation [16, 17, 18], glacier monitoring [19], landslides [20], soil compaction rate [21] or atmosphere estimation [4]. As happened with classical DInSAR, the achievable velocity map reliability also depends on the pixels affected by decorrelation phenomena. The displacement information cannot thus be exploited from all pixels within the illuminated scenario, as only a limited number of them, the so-called persistent scatterers, fulfill the phase quality requirements to be included in the PSI processing. Two main criteria are available for the estimation of pixels' phase quality: these are the coherence stability [12, 18] and the permanent scatterer (PS) approach [6]. The former makes use of the estimated coherence maps from the multi-looked interferograms, which can be directly related with the standard deviation of the interferometric phase. The multi-look (ML) used, which basically consists of applying a boxcar window, reduces the resolution of the interferograms depending on the averaging factor employed. This fact impacts the pixel selection step, leading to an inherent reduction of the resolution during the detection of persistent scatterers. For this reason, this approach is typically addressed as low-resolution PSI. The latter relates the phase dispersion of those scatterers presenting high values of signal-to-noise ratio (SNR) with the amplitude dispersion (\(D_{A}\)) estimator [6], which basically corresponds to a measure of the pixels' amplitude stability. Pixels stable in amplitude are assumed to be reliable in phase. Since the multi-looking of data is not required in that case, the resolution of the original images is preserved during the detection of persistent scatterers. For this reason, this method is typically addressed as full-resolution PSI. The choice of the pixel selection criterion basically depends on the number of acquisitions at disposal, on the resolution required and on the nature of the scenario to be monitored. On the one hand, the coherence stability method ensures accurate estimations of the phase statistics, even when a reduced number of SAR images is available. In contrast, the PS approach demands a larger number of SAR images to be reliable, typically more than \(20\)[6]. On the other hand, the coherence stability criterion performs better over environments with the predominance of distributed targets; this is when multiple scatters are present within a resolution cell.