Robust recovery of synthetic aperture radar data from uniformly under-sampled measurements

In this paper, we propose a novel robust sparse-recovery technique that allows sub-Nyquist uniform under-sampling of wide-bandwidth radar data in real time (single observation). Although much of the information is lost in the received signal due to the low sampling rate, we hypothesize that each wide- bandwidth radar data record can be modeled as a superposition of many backscattered signals from reflective point targets in the scene. In other words, our proposed technique is based on direct sparse recovery via orthogonal matching pursuit using a special dictionary containing many time-delayed versions of the transmitted probing signal. Using data from the U.S. Army Research Laboratory (ARL) Ultra-Wideband (UWB) synthetic aperture radar (SAR), we show that the proposed sparse-recovery model- based (SMB) technique successfully models and synthesizes the returned radar data from real-world scenes using only an analytical waveform that models the transmitted signal and a handful of reflectivity coefficients. More importantly, the reconstructed SAR imagery using the SBM technique with data sampled at only 20% of the original sampling rate has a comparable signal-to-noise ratio (SNR) to the original SAR imagery. For comparison purpose, the paper also presents SAR images recovered from conventional interpolation techniques and the standard random projection based compressed sensing technique, both of which resulted in very poor SAR image quality at the same sub-Nyquist sampling rate (20%).