PURPOSE: Diffusion Spectrum Imaging enables to reconstruct the ensemble average propagator (EAP) at the expense of having to acquire a large number of measurements. Compressive sensing offers an efficient way to decrease the required number of measurements. The purpose of this work is to perform a thorough experimental comparison of three sampling strategies and six sparsifying transforms to show their impact when applied to accelerate compressive sensing-diffusion spectrum imaging. METHODS: We propose a novel sampling scheme that assures uniform angular and random radial q-space samples. We also compare and implement six discrete sparse representations of the EAP and thoroughly evaluate them on synthetic and real data using metrics from the full EAP, kurtosis, and orientation distribution function. RESULTS: The discrete wavelet transform with Cohen-Daubechies-Feauveau 9/7 wavelets and uniform angular sampling in combination with random radial sampling showed to be better than other tested techniques to accurately reconstruct the EAP and its features. CONCLUSION: It is important to jointly optimize the sampling scheme and the sparsifying transform to obtain accelerated compressive sensing-diffusion spectrum imaging. Experiments on synthetic and real human brain data show that one can robustly recover both radial and angular EAP features while undersampling the acquisition to 64 measurements (undersampling factor of 4). Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.