# High Performance Computing in Satellite SAR Interferometry: A Critical Perspective
## 2 SAR Interferometric Processing
### Interferograms Formation and Filtering  
Once two SAR images are co-registered, the corresponding coherence map and SAR interferogram can be straightforwardly generated, with a limited computational cost. The formed interferograms can be affected by significant decorrelation noise artefacts, which have different sources. Loss of correlation can be due to thermal noise, misregistration errors, effects of the slightly different illumination geometries of the interfering SAR images (baseline decorrelation), the time span of the interferogram (temporal decorrelation), as well as a non-perfect overlap of the two SAR images azimuthal spectra. Several noise filtering techniques [52; 53; 54; 55; 56] can be applied to mitigate the noise artefacts in the generatedinterferograms at the expense of an increased computational burden. Most of them operate on single-channel SAR interferograms (i.e., without considering the temporal mutual relationships among a set of interferograms sharing the same set of SAR data). Only a few operate jointly on multi-temporal SAR interferograms (e.g., [57; 58]). In the latter case, the generation of a large group of time-redundant interferograms is required to obtain enhanced noise-filtering performance with respect to the single-channel case, thus determining a drastic increase in the computational load. Overall, noise-filtering methods rely on the knowledge of the statistics of multilook SAR interferograms, which can be characterized via a probability density function expressible in closed forms, see [59; 60; 61]. Nonetheless, in most cases, a first-order statistical characterization as a function of the noise standard deviation, which depends on the coherence and the number of independent looks used for the coherence computation, can generally be sufficient to implement most of the proposed algorithms. The multilook processing techniques belong to this class, which have been proven effective for noise reduction, even though this is paid in terms of a decrease in the image spatial resolution and the relevant InSAR products.  
Noise filtering constitutes a preliminary step before phase unwrapping. Indeed, the complex multi-look operation usually involves an averaging on neighbouring SAR pixels, hence reducing the spatial resolution of the interferograms.  
A frequently used option is provided by [PERSON]'s frequency-domain algorithm [52], which is an empirical approach originally introduced for geophysical applications. A modification of [PERSON]'s filter that relies on an adaptive choice of the filtering factor \(\alpha\) (which, in turn, depends on the spatial coherence \(\rho\)) has also been proposed [62]. Other filters, such as the median filter [63] and the two-dimensional Gaussian filter, also reduce noise while performing multilook operations.  
[PERSON] et al. 1998 [59] proposed a self-adaptive filter based on local gradient slope estimation that can improve noise-filtering performance by exploiting directional characteristics of an InSAR interferogram. Several adaptations and relevant improvements of the [PERSON] filter have subsequently been proposed in literature over time [64; 61].  
Non-local InSAR algorithms (NL-InSAR) are often used at the filtering stage. Introduced initially to denoise optical images [65], non-local mean filters have also become increasingly popular for their capacity to preserve details discriminating statistically homogeneous pixels in a SAR image. They have been extensively applied to denoise amplitude SAR images [66], interferograms [67], and polarimetric [68] data; more recently, they have been applied to denoise stacks of SAR data for differential SAR interferometry applications [69].