# High Performance Computing in Satellite SAR Interferometry: A Critical Perspective
## 2 SAR Interferometric Processing
### Multi-Temporal Interferometric SAR Techniques  
Multi-temporal interferometric SAR (MT-InSAR) algorithms can broadly be grouped into two classes: (i) persistent scatters (PS) methods, primarily devoted to the analysis of point-wise scatters, and (ii) small baseline (SB) methods, mainly dealing with distributed scatterers (DS) within the resolution cell [18]. The PS methods allow analyzing the ground deformation at the full sensor resolution (single-look scale), assuming that in the resolution cell a dominant scatterer is present that preserves its phase characteristics over the entire timeframe covered by the SAR data time-series [19; 20; 21; 22]. Since, for such targets, the decorrelations effects are negligible, no constraints on both temporal and spatial baselines are necessary; therefore, the interferometric couples are usually generated by referring each acquisition to a single reference image, so that, given a set of \(N\) images, \(N-1\) interferograms are produced. Conversely, the small baseline (SB) methodologies analyze the ground displacement in the case of distributed targets within the resolution cells of the imaged SAR scenes [23; 24; 25; 26; 27]. Unlike PS targets, DSs are severely affected by spatial and temporal decorrelation effects that introduce noise in the generated interferograms [16]. Therefore, SB methods select and process only InSAR data pairs characterized by short temporal and spatial baselines to limit such decorrelation effects. For this reason, interferograms are not generated with respect to a single reference image (as for PS), but each selected data pair has its reference; given a set of \(N\) images, SB methods will generate a number \(M\) of interferograms larger than \(N-1\). Moreover, a complex multi-look operation is usually carried out to further mitigate the decorrelation phase noise effects. The pioneering algorithm known as small baseline subset (SBAS) [23] belongs to SB methods. It exploits a sequence of SB multi-look interferograms to recover the ground displacement time-series of a set of DS. Depending on the constraints applied to select the interferograms, SAR data might be arranged in several disjointed (time-overlapped) subsets separated by long baselines. In these cases, the SBAS algorithm applies the least squares (LS) inversion method of the SB interferograms by linking the independent subsets via a singular value decomposition (SVD) approach [87]. Several SB algorithms have been proposed in the last 20 years, including methods for analyzing the ground deformations related to intermittent DS and implementing weighted least squares (WLS) inversion operations [88; 89]. Among the methods for analyzing DS targets, the SqueezeSAR technique [25] operates on interferograms computed at the _single-look_ spatial scale. It implements an adaptive spatial multi-look operation that relies on the preliminary computation of a set of statistically homogenous (SHP) SAR pixels. SqueezeSAR also includes the phase triangulation algorithm (PTA), which is applied to multilook interferograms to obtain an estimate of an optimized set of phases associated with every single available SAR image. These methods significantly increase the computational burden, because they require extra operations performed at the single-look scale. On the one hand, the SHPs must be identified by analyzing the single look SAR interferograms. On the other hand, estimating the optimized phases through PTA requires the availability of the whole set of SAR interferograms to compute the entire covariance matrix [25]. Recent works (e.g., [90]) on PTA optimization have focused on computationally efficient approaches with no substantial InSAR product degradation. As far as the SqueezeSAR is concerned, a few alternative methods, which allow obtaining optimized multilook interferograms by using only reduced sets of multilook SB interferograms, have been proposed [91]. A substantial reduction in the computational load of these methods with respect to SqueezeSAR is noticeable.