An ambiguity-free direction-of-arrival (DOA) estimation scheme is proposed for sparse uniform linear arrays under low signal-to-noise ratios (SNRs) and non-stationary broadband signals. First, for achieving better DOA estimation performance at low SNRs while using non-stationary signals compared to the conventional frequency-difference (FD) paradigms, we propose parameterized time-frequency transform-based FD processing. Then, the unambiguous compressive FD beamforming is conceived to compensate the resolution loss induced by difference operation. Finally, we further derive a coarse-to-fine histogram statistics scheme to alleviate the perturbation in compressive FD beamforming with good DOA estimation accuracy. Simulation results demonstrate the superior performance of our proposed algorithm regarding robustness, resolution, and DOA estimation accuracy.