Duplex ultrasonography is a mode of medical ultrasonography that allows one to visualize, at the same time, the inner structure of the body (B-mode) and the blood flow at a particular point in the body (Doppler mode). This mode requires a strategy for alternating B-mode and flow emissions. Traditional strategies either halve the maximum measurable velocity or introduce gaps in the flow data. The objective of this article is to propose a completely original method based on compressive sensing for reconstructing the Doppler signal segment by segment. Our approach is based on randomly alternating B-mode and flow emissions. The influence of the different parameters on the reconstruction quality is studied in detail. The technique is evaluated and its feasability is validated in simulation and from experimental in vivo data. It is also compared to the only method from the literature, proposed by Jensen, that reconstructs blood velocity estimates from sparse data sets.