19F-MRSI has the potential to track multiple perfluorocarbon nanoemulsions simultaneously, but existing 19F-MRSI schemes have been limited to CSI, which provides a poor tradeoff between resolution and scan time. In this work, a novel method is proposed to enable fast high-resolution 19F-MRSI. In the proposed method, (k,t)-space is sampled rapidly in EPSI trajectories; data processing is accomplished using a union-of-subspaces model with pre-learned spectral basis. The proposed method has been evaluated using simulation and experimental data, producing encouraging results. The proposed method may open up new opportunities for simultaneous tracking of different labeled cell populations in vivo.