Compressive sensing and generalized likelihood ratio test in SAR tomography

Synthetic Aperture Radar (SAR) interferometry has been the subject of an intensive development in the last years thanks to crucial applications in the area of risk monitoring. The emergence of very high resolution X-Band sensors has increased the interest in application to urban area. Advances of SAR interferometry has been provided by the extension toward SAR tomography. By transforming classical 2-D SAR imaging into higher dimensional (space-time) imaging, it offers the possibility to reconstruct the 3-D/4-D scattering distribution and to detect point clouds for reconstructing single buildings and infrastructures and for the monitoring of their long term deformation. The resolution provided by classical SAR tomographic methods may show limitations in the detection of point clouds. To improve the performance of the tomographic tools super-resolution Compressive Sensing (CS) algorithms have been recently proposed. The literature, however, lacks of an assessment of the improvement of CS over classical point could detection schemes based on classical matched filter as well as of possible indications about the development of a CS algorithm able to guarantee a fixed false alarm probability. This work aims to provide a contribution along this line.