## 2 Differential Radar Interferometry for Deformation Monitoring in Cultural Heritage Sites
### Large-Scale Deformation Monitoring over Heritage Sites  
While analyzing the deformation in heritage sites, the core area together with surroundings should be monitored as a whole, considering the long-term and regional-scale influences of environmental and anthropogenic factors. Multi-Temporal Synthetic Aperture Radar Interferometry (MT-InSAR), using a time-series of Synthetic Aperture Radar (SAR) images acquired over the same area to extract displacement information, overcomes the intrinsic limitations of conventional differential radar interferometry in terms of geometrical and temporal de-correlation, as well as atmospheric artifacts. It provides an effective solution to measure large-scale surface deformations with accuracy up to the millimeter level [16; 17; 18; 19; 20; 21; 22; 23; 24].  
Based on the different combination modes of interferometric pairs, MT-InSAR methods can be classified into single-master image mode, multi-master image mode and hybrid mode, respectively. The representative of the single-master image mode is Persistent Scatterers SAR interferometry (PS-InSAR) [17; 19; 25; 26]. This method identifies point targets whose phases, due to de-correlation, vary little, even with large temporal and spatial baselines [27]. These point targets, exhibited as dominant scatterers in ground resolution elements, often correspond to man-made structures, such as boulders, outcrops, _etc._ Hence, PS-InSAR is applicable to cultural heritage sites with an abundance of structures and archaeological remains on the ground. The representative of the multi-master image mode is Small Baseline SAR interferometry (SB-InSAR) [16; 21]. SB-InSAR primarily deals with distributed scatterers (DSs) represented by bare soil, debris areas and sparsely vegetated land, which share the same statistical backscattering behavior within a given spatial range [27]. Therefore, SB-InSAR shows its advantage in deformation monitoring over cultural heritage sites in non-urban areas owing to the capability of DS target extraction. In general, the scattering characteristics of real terrains are complex, and hence, a hybrid mode needs to be developed combining both PS and DS to increase the spatial density of detected targets in observed scenarios. The representatives of the hybrid mode are found in the combined MT-InSAR method presented by [PERSON] [15] and SqueezeSAR initiated by [PERSON] _et al._[18], respectively. The hybrid mode widens the field of application for heritage sites located in urban and non-urban areas, especially in archaeological sites characterized by a low density of exposed structures on the ground or archaeological remains widely spread over rural landscapes. Furthermore, since the hybrid mode makes full use of PS and DS to improve the probability of identifying measuring targets, it is more feasible to monitor superficial deformation caused by inner instability or the collapse of heritage structures that lay buried below the surface. So far, a number of studies conducted in Rome, Mexico, Venice and several other cities have demonstrated the effectiveness of MT-InSAR for deformation monitoring and preventative diagnosis of cultural heritage sites [12; 13; 14; 28; 29; 30; 31; 32].