# High Performance Computing in Satellite SAR Interferometry: A Critical Perspective
## 2 SAR Interferometric Processing
### Image Coregistration  
Image coregistration consists in aligning two (or more) images so that homologous pixels in all images correspond to the same sensed target on the ground. If we want to extract information by comparing images, we need to compare measurements associated with the same ground portion. Due to the improved spatial resolution and reduced revisit times of the current SAR platforms, the coregistration of multiple SAR images may result in a computationally intensive task.  
This is a fundamental and necessary stage in the InSAR processing chain since SAR images of a given area on the ground acquired from different spatial positions are subject to different geometrical distortions, which depend on a combination of local topography and acquisition geometry. For this reason, the coregistration procedure is a space-variant operation that cannot be reduced to a single constant image shift; instead, it requires a distortion of the pixel grid (warping) to accommodate the different viewing geometry. Moreover, a local sub-pixel shift (in the order of a small fraction of a pixel) is usually required to achieve a good interferometric coherence, thus affecting the relevant computational burden.  
The SAR image coregistration operation is usually performed in two steps: (i) warp function computation, i.e., computation of the functional relation that maps the geometry of one image into that of the other one; and (ii) resampling of one image (secondary one) at the inter-pixel locations according to the warp function.  
A classical approach to compute the warp function consists in matching many small patches in both the images to be coregistered using _cross-correlation_ techniques [46; 47]. Since this must be done at the sub-pixel level, an up-sampling of the images is required. These measurements are subsequently used to estimate the unknown coefficients of a bivariate polynomial modelling the spatial warp transformation.  
Alternatively, the warping function can be computed via a _geometric_ approach [48]. This is acheived by finding the position of a given point on the ground in both the primary and the secondary images following the range-Doppler equations and using a digital elevation model (DEM), along with precise information on the sensor platform ephemerides.  
The main advantage of the second approach is to be independent of the data, so be suitable also when large areas of the SAR images are incoherent. Moreover, it is also less computationally expensive since the solution of the range-Doppler equations can be completed efficiently and does not require data oversampling, see [49].  
After the warping function computation, resampling of the secondary image to align it to the primary one is necessary. This is usually achieved via convolution of the secondary image with a 2D interpolation kernel or a cascade of two one-dimensional ones. The latter case is suitable for line-by-line and column-by-column processing, thus increasing the computational performance.  
Finally, we note that the typical high Doppler rate in azimuth of data acquired in TOPS modes poses very stringent requirements to the coregistration processing step. In this case, an additional fine (rigid) azimuth shift must be computed with very high accuracy. Enhanced spectral diversity (ESD) techniques [50; 51] have become very popular to face this problem, especially with the advent of Sentinel-1 sensors. Although capable of reaching very high accuracy, the ESD method can be impaired by loss of interferometric coherence in the data and/or by the presence of a significant ground deformation signal in the data.