Diffusion spectrum imaging (DSI) offers detailed information on complex distributions of intravoxel fiber orientations at the expense of extremely long imaging times (1 hour). It is possible to accelerate DSI by sub-Nyquist sampling of the q-space followed by nonlinear reconstruction to estimate the diffusion probability density functions (pdfs). Recent work by Menzel et al. imposed sparsity constraints on the pdfs under wavelet and total variation (TV) transforms. As the performance of Compressed Sensing (CS) reconstruction depends strongly on the level of sparsity in the selected transform space, a dictionary specifically tailored for sparse representation of diffusion pdfs can yield higher fidelity results. To our knowledge, this work is the first application of adaptive dictionaries in DSI, whereby we reduce the scan time of whole brain DSI acquisition from 50 to 17 min while retaining high image quality. In vivo experiments were conducted with the novel 3T Connectome MRI, whose strong gradients are particularly suited for DSI. The RMSE from the proposed reconstruction is up to 2 times lower than that of Menzel et al.'s method, and is actually comparable to that of the fully-sampled 50 minute scan. Further, we demonstrate that a dictionary trained using pdfs from a single slice of a particular subject generalizes well to other slices from the same subject, as well as to slices from another subject.