## 2 Overview of InSAR Methodology
### Multi-Pass InSAR Techniques for the Retrieval of Surface Displacement Time-Series  
In this section, we provide a short overview of advanced multi-pass InSAR techniques [71; 99; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109], allowing to retrieve the temporal evolution of deformation by properly combining sequences of differential SAR interferograms. Two main categories of advanced DInSAR techniques for deformation time-series generation have been proposed. They are often referred to as persistent scatterer (PS) [99; 100; 101; 102] and small baseline (SB) [71; 103; 104; 105; 106] techniques, respectively, although a solution that incorporates both PS and SB approaches has also recently been proposed [107]. Furthermore, more recently, the SqueezeSAR method [108], which operates on interferograms computed at the same spacing of the full resolution ones but following an ad-hoc Low-Pass filtering step, has been introduced. SqueezeSAR implements a statistical approach, which exploits both phase and amplitude information, to directly retrieve from all the possible interferograms, i.e., without imposing baseline constraints, the noise-filtered phase values associated with the SAR acquisitions. To this aim, the phase triangulation method [108] is applied. The reconstructed phase maps related to each SAR acquisitions, properly post-processed, lead to the generation of surface displacement time-series. More precisely, PS algorithms select all the interferometric data pairs about a single common master image, without imposing any constraint on the temporal and spatial separation (baseline) among the orbits. In this case, the analysis is carried out at the full spatial resolution scale and is focused on the pixels containing a single dominant scatterer. Conversely, for what concerns the SB techniques, the differential SAR interferograms are generated by considering multiple-master images, in order to have interferometric data pairs with small temporal and spatial baselines. Accordingly,  
Figure 9: COSMO-SkyMed differential interferogram (in radar coordinates) computed from SAR acquisitions collected over Shanghai megacity on 8 January and 9 February 2014.  
distributed targets can also be investigated and the analysis may exploit both single-look and multi-look interferograms. Among the SB techniques, a popular approach is the one referred to as Small BAseline Subset (SBAS) [71] that allows producing LOS-projected mean deformation velocity maps and corresponding displacement time-series. The SBAS technique has been initially developed to analyse multi-look (complex average) interferograms [71] and it has subsequently been extended to work with full-resolution interferograms [109], with the aim to analyse localized deformation signals affecting, for instance, single buildings or artificial structures. As previously said, the SBAS approach relies on imposing constraints on the spatial and temporal baselines of SAR data pairs used to produce the interferograms. Accordingly, the selected SAR data pairs may be arranged in (few) subsets that are separated by large baselines. These subsets turn out to be independent of each other (since no suitable interferogram that connects SAR images belonging to different subsets exists). The presence of subsets gives rise to an underdetermined problem for the time-series inversion, which can be solved by searching for a minimum norm least squares solution via the SVD method [80]. In 2015, an improved SBAS processing chain, which complements the Extended Minimum Cost Flow (EMCF) [110] space-time phase unwrapping operations with an innovative space-time noise-filtered approach and an optimized selection of InSAR data to be inverted, has also been proposed [68]. To provide an example of the effectiveness of the noise-filtered approach implemented in [68], we show in Figure 11 a comparison between conventional and noise-filtered ASAR/ENVISAT differential SAR interferograms detecting the 6 April 2009, Mw. 6.3 L'Aquila (Italy) earthquake.