One-bit compressive sensing with time-varying thresholds in synthetic aperture radar imaging

In this study, the authors introduce a new framework for 1-bit compressed synthetic aperture radar (SAR) imaging by using time-varying thresholding. They show how to recover sparse SAR images from noisy measurements which have been quantised to 1-bit with time-varying thresholds. In the conventional 1-bit compressive sensing (CS) SAR imaging methods, 1-bit quantisation is implemented by comparing the received signal to a zero threshold. This makes the information about the magnitude of the signal to be lost and exact signal recovery becomes impossible. One-bit quantisation with time-varying thresholds allows them to reconstruct the magnitude of the signal more accurately and an explicit unit-norm constraint is no longer required in the proposed optimisation formulation. Using the proposed approach, the authors formulate 1-bit CS SAR imaging reconstruction problem as an unconstrained optimisation problem where the objective function includes an l(2) data-fidelity term and a non-smooth regularisation function. In order to solve this unconstrained optimisation problem, they use variable splitting and the alternating direction method of multipliers based approach which is computationally efficient and easy to implement. The results from experiments with synthetic and real SAR images validate the effectiveness of the proposed method named as BCST-SAR (binary CS with time-varying thresholds in SAR imaging).