Hyperpolarized (HP) (3) He and (129) Xe are two gases with different fluid dynamic properties, which can be used as tracers for airflow measurement in the lungs with phase contrast velocimetry MRI sequences. In this work, in vivo measurements of velocity maps of airflow in the upper airways and first bronchi of healthy volunteers were obtained with both gases and compared. To reduce the acquisition time, a Compressed Sensing (CS) based acquisition and reconstruction algorithm was developed and optimized for flow measurement in three directions by including the sparsity of the complex difference images as prior knowledge. CS simulations on retrospectively under-sampled images demonstrated a better reconstruction with the inclusion of the complex difference terms in the cost function. The technique was then validated with a prospective acquisition study providing artifact free maps with acceleration factors up to 3. The presented technique opens up the possibility to map velocity inside human lungs. The results are of interest for the validation of computational fluid dynamics flow simulations and for understanding the spatio-temporal evolution of airflow patterns in the airways in vivo with different gas mixtures.