While many useful microstructural indices, as well as orientation
distribution functions, can be obtained from multi-shell dMRI data, there is
growing interest in exploring the richer set of microstructural features that
can be extracted from the full ensemble average propagator (EAP). The EAP can be
readily computed from diffusion spectrum imaging (DSI) data, at the cost of a
very lengthy acquisition. Compressed sensing (CS) has been used to make DSI more
practical by reducing its acquisition time. CS applied to DSI (CS-DSI) attempts
to reconstruct the EAP from significantly undersampled q-space data. We present
a post mortem validation study where we evaluate the ability of CS-DSI to
approximate not only fully sampled DSI but also multi-shell acquisitions with
high fidelity. Human brain samples are imaged with high-resolution DSI at 9.4T
and with polarization-sensitive optical coherence tomography (PSOCT). The latter
provides direct measurements of axonal orientations at microscopic resolutions,
allowing us to evaluate the mesoscopic orientation estimates obtained from
diffusion MRI, in terms of their angular error and the presence of spurious
peaks. We test two fast, dictionary-based, L2-regularized algorithms for CS-DSI
reconstruction. We find that, for a CS acceleration factor of
R
=3, i.e., an acquisition with 171 gradient directions, one of
these methods is able to achieve both low angular error and low number of
spurious peaks. With a scan length similar to that of high angular resolution
multi-shell acquisition schemes, this CS-DSI approach is able to approximate
both fully sampled DSI and multi-shell data with high accuracy. Thus it is
suitable for orientation reconstruction and microstructural modeling techniques
that require either grid- or shell-based acquisitions. We find that the
signal-to-noise ratio (SNR) of the training data used to construct the
dictionary can have an impact on the accuracy of CS-DSI, but that there is
substantial robustness to loss of SNR in the test data. Finally, we show that,
as the CS acceleration factor increases beyond
R
=3, the
accuracy of these reconstruction methods degrade, either in terms of the angular
error, or in terms of the number of spurious peaks. Our results provide useful
benchmarks for the future development of even more efficient q-space
acceleration techniques.