Diffusion spectrum imaging (DSI) is a promising tool for estimation of white-matter fiber structure. DSI also allows for model-based estimation of several microstructure measures. However, the long data acquisition time associated with DSI limits its application in stroke patients. Here we combine a simultaneous multi-slice acquisition with an undersampled q-space acquisition and dictionary reconstruction to accelerate DSI. The two complementary acceleration schemes allow for a rapid 5.5 minute DSI acquisition in stroke subjects. We used generalized fractional anisotropy and microstructure measures computed from the NODDI model to evaluate the rapid DSI framework in stroke patients.