Persistent Scatterer Density by Image Resolution and Terrain Type

Persistent Scatterer Interferometry (PSI) is a powerful time-series InSAR technique to characterize subsidence in "difficult" data sets over diverse sources including volcanic activity, landslides, natural resource extraction, and land reclamation. By identifying stable pixels, known as persistent scatterers (PS), we can observe the underlying ground deformation in areas that would otherwise be limited by temporal and spatial decorrelation. As a result, the performance of PSI depends heavily on the density of the points identified as PS, which depends on two main factors: image resolution and the reflectivity and rates of decorrelation in different types of terrain. However, much previous understanding of the relationship between PS density, image resolution, and terrain type has been rather qualitative. Deeper knowledge of PS statistics and their relation to image resolution and terrain is necessary if we wish to design efficient systems for future satellite missions, as well as designing more effective PS detection schemes.

In this work, we establish a quantitative link between PS density and these two factors, empirically and theoretically. First, we analyze the behavior of PS density for different terrain types (urban, mixed, and rural) at different image resolutions. We then present a simple theoretical framework for predicting the change in PS density by estimating the change in the pixel signal-to-clutter ratio (SCR) at each bandwidth, calculated by the ratio of the expected PS power to the clutter power and the power of other noise sources. This model adheres to the empirical results within 50% error, and rather closer for high SCR points that form the desired network of PS points. Additionally, we find that the probability density functions (PDFs) of PS occurrence with respect to SCR for each region are approximately independent of system bandwidth. Thus, the increase in PS density is roughly proportional to increased bandwidth due to a higher pixel density in finer resolution images. Finally, knowledge of the SCR PDFs should allow us to optimize PS selection criteria. These results lay the groundwork for a more quantitative understanding of the relationship between PS density—and by extension, PSI performance—and image resolution and terrain type.