Focusing SAR images by compressive sensing: Study of interferometric properties

In this work we study the problem of focusing Synthetic Aperture Radar (SAR) images by means of Compressive Sensing (CS). The presented technique is introduced as an alternative to the traditional focusing methods, suggesting new modes for data acquisition in a more efficient configurations or on-board processing in case of spaceborne sensors. In this paper the method is tested on both simulated and real images acquired by a Ground Based Synthetic Aperture Radar (GB-SAR), for which images of reduced size can be generated with no difficulty. Results of comparison of CS processing with an exact focusing algorithm are shown in terms of root mean square error of amplitude and phase as a function of the number of focused targets and undersampling of the acquisition lines. Coherence of a CS-processed couple of images is also evaluated. The purpose of the paper is to show the potential of CS applied to SAR systems, regardless (at the moment) of the efficiency in computational load. In particular, we show that the image can be reconstructed without loss of resolution after dropping a fair percentage of the received pulses.