Dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) ideally requires a high spatial and high temporal resolution, but hardware limitations prevent acquisitions from simultaneously achieving both. Existing image reconstruction techniques can artificially create spatial resolution at a given temporal resolution by estimating data that is not acquired, but, ultimately, spatial details are sacrificed at very high acceleration rates. The purpose of this paper is to introduce the concept of spatial subspace reconstructions (SPARS) and demonstrate its ability to reconstruct high spatial resolution dynamic images from as few as one acquired radial spoke per dynamic frame. Briefly, a low-temporal-high-spatial resolution organization of the acquired raw data is used to estimate a spatial subspace in which the high-temporal-high-spatial ground truth data resides. This subspace is then used to estimate entire images from single k-space spokes. In both simulated and human in-vivo data, the proposed SPARS reconstruction method outperformed standard GRASP and GRASP-Pro reconstruction, providing a shorter reconstruction time and yielding higher accuracy from both a spatial and temporal perspective.