Robust Sparse Sensing Using Weather Radar

The ability of a weather radar to detect weak echoes is limited by the presence of noise or unwanted echoes. Some of these unwanted signals originate externally to the radar system, such as cosmic noise, radome reflections, interference from co-located radars, and power transmission lines. The internal source of noise in microwave radar receiver is mainly thermal. The thermal noise from various microwave devices in the radar receiver tends to lower the signal-to-noise ratio, thereby masking the weaker signals.

Recently, the compressed sensing (CS) technique has emerged as a novel signal sampling paradigm that allows perfect reconstruction of signals sampled at frequencies lower than the Nyquist rate. Many radar and remote sensing applications require efficient and rapid data acquisition. The application of CS to weather radars may allow for faster target update rates without compromising the accuracy of target information. In our previous work, we demonstrated recovery of an entire precipitation scene from its compressed-sensed version by using the matrix completion approach.

In this study, we characterize the performance of such a CS-based weather radar in the presence of additive noise. We use a signal model where the precipitation signals form a low-rank matrix that is corrupted with (bounded) noise. Using recent advances in algorithms for matrix completion from few noisy observations, we reconstruct the precipitation scene with reasonable accuracy. We test and demonstrate our approach using the data collected by Iowa X-band Polarimetric (XPOL) weather radars.