A new method for flow velocity mapping is presented here. Instead of the conventional approach of employing two images (velocity sensitive and control) to generate velocity information, in the new method one determines the velocity directly from a single-shot acquisition by solving an inverse problem. This technique is a variant of single-shot parameter assessment by retrieval from signal encoding (SS-PARSE). The results of simulation and phantom studies show strong agreement with the actual velocities. The prototype method can measure velocities in the range of -50 to 50 cm/s, which is roughly appropriate for future applications in dynamic blood flow measurement in carotid arteries.