Can Compressed Sensing Be Applied To Dual-Polarimetric Weather Radars?

The recovery of sparsely-sampled signals has long attracted considerable research interest in various fields such as reflection seismology, microscopy, and astronomy. Recently, such recovery techniques have been formalized as a sampling method called compressed sensing (CS) which uses few linear and non-adaptive measurements to reconstruct a signal that is sparse in a known domain. Many radar and remote sensing applications require efficient and rapid data acquisition. CS techniques have, therefore, enormous potential in dramatically changing the way the radar samples and processes data. A number of recent studies have investigated CS for radar applications with emphasis on point target radars, and synthetic aperture radar (SAR) imaging. CS radar holds the promise of compressing-while-sampling, and may yield simpler receiver hardware which uses low-rate ADCs and eliminates pulse compression/matched filter. The need of fewer measurements also implies that a CS radar may need smaller dwell times without significant loss of information. Finally, CS radar data could be used for improving the quality of low-resolution radar observations. In this study, we explore the feasibility of using CS for dual-polarimetric weather radars. In order to recover a signal in CS framework, two conditions must be satisfied: sparsity and incoherence. The sparsity of weather radar measurements can be modeled in several domains such as time, frequency, joint time-frequency domain, or polarimetric measurement domains. The condition of incoherence relates to the measurement process which, in a radar scenario, would imply designing an incoherent transmit waveform or an equivalent scanning strategy with an existing waveform. In this study, we formulate a sparse signal model for precipitation targets as observed by a polarimetric weather radar. The applicability of CS for such a signal model is then examined through simulations of incoherent measurements along with real weather data obtained from Iowa X-band Polarimetric (XPOL) radar units.