Robert Jones^{1}, Giorgia Grisot^{1,2}, Jean Augustinack^{1}, David A. Boas^{1,3}, Bruce Fischl^{1,4}, Hui Wang^{1}, Berkin Bilgic^{1}, and Anastasia Yendiki^{1}

Compressed
sensing algorithms for accelerating DSI acquisitions (DSI-CS) have
helped bring DSI into the realm of clinical feasibility. Here, we
assess the efficacy of dictionary-based CS methods in reconstructing
high resolution *ex
vivo*
DSI of human brain blocks, and provide validation of *ex
vivo*
DSI-CS with ground truth optical imaging. We find that reconstruction
accuracy, computation time and inter-subject dictionary
generalizability are comparable to *in
vivo* results,
and that SNR appears influential in determining the limit of
attainable reconstruction quality. We also show that fiber
orientation estimates of reconstructed data are as accurate as
fully-sampled estimates at a microscopic level.

dMRI:
We cut two blocks (3x2x2cm) from different anatomical regions of the
same *ex
vivo*,
fixed human hemisphere (Fig. 1). We imaged each block on a 9.4T
Bruker magnet with |G|_{max}=480
mT/m, using a 3D EPI sequence (δ=15ms, Δ=19ms, 514 directions,
b_{max}=40000s/mm^{2},
0.25mm iso resolution) for full DSI q-space encoding with one b=0
image. A surface coil was used, leading to a dependence of SNR on
distance from the coil. This allowed us to investigate the
relationship between SNR and reconstruction accuracy.

PS-OCT:
Following dMRI, we imaged a 2x1.5x0.5cm section of one brain block
with PS-OCT. PS-OCT acquisition and analysis was performed as
described previously ^{10,11},
yielding direct measurements of in-plane axonal orientation at 10μm
in-plane and 75μm through-plane resolution.

Dictionary
Training & Reconstruction:
We undersampled the DSI data by an acceleration factor of R=3, and
used two L2-based algorithms for CS reconstruction described in ^{7},
with dictionary training sets derived from PDFs from a single slice
of fully-sampled data. We compared Principal Component Analysis (PCA)
reconstruction, and Tikhonov-regularized pseudoinverse reconstruction
using either dictionaries trained with the K-SVD algorithm^{12}
[PINV(KSVD)] or the training PDFs themselves as the dictionary
[PINV(PDF)]. We reconstructed slices of sample A using dictionaries
trained on either sample A or sample B. We computed the normalized
RMSE, in terms of both PDFs and q-space, between the fully-sampled
data and those reconstructed with PINV(KSVD), PINV(PDF) and PCA.

1. Wedeen VJ, Hagmann P, Tseng WY, Reese TG, Weisskoff RM. Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magnetic resonance in medicine. 2005 Dec;54(6):1377-86.

2.Setsompop K, Cohen-Adad J, Gagoski BA, Raij T, Yendiki A, Keil B, Wedeen VJ, Wald LL. Improving diffusion MRI using simultaneous multi-slice echo planar imaging. Neuroimage. 2012 Oct 15;63(1):569-80.

3. Setsompop K, Gagoski BA, Polimeni JR, Witzel T, Wedeen VJ, Wald LL. Blipped‐controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g‐factor penalty. Magnetic resonance in medicine. 2012 May 1;67(5):1210-24.

4. Keil B, Blau JN, Biber S, Hoecht P, Tountcheva V, Setsompop K, Triantafyllou C, Wald LL. A 64‐channel 3T array coil for accelerated brain MRI. Magnetic resonance in medicine. 2013 Jul;70(1):248-58.

5. McNab JA, Edlow BL, Witzel T, Huang SY, Bhat H, Heberlein K, Feiweier T, Liu K, Keil B, Cohen-Adad J, Tisdall MD. The Human Connectome Project and beyond: initial applications of 300 mT/m gradients. Neuroimage. 2013 Oct 15;80:234-45.

6. Tobisch A, Stirnberg R, Harms RL, Schultz T, Roebroeck A, Breteler MM, Stöcker T. Compressed Sensing Diffusion Spectrum Imaging for Accelerated Diffusion Microstructure MRI in Long-Term Population Imaging. Frontiers in neuroscience. 2018;12.

7. Bilgic B, Chatnuntawech I, Setsompop K, Cauley SF, Yendiki A, Wald LL, Adalsteinsson E. Fast dictionary-based reconstruction for diffusion spectrum imaging. IEEE transactions on medical imaging. 2013 Nov;32(11):2022-33.

8. Menzel MI, Tan ET, Khare K, Sperl JI, King KF, Tao X, Hardy CJ, Marinelli L. Accelerated diffusion spectrum imaging in the human brain using compressed sensing. Magnetic Resonance in Medicine. 2011 Nov;66(5):1226-33.

9. Bilgic B, Setsompop K, Cohen-Adad J, Yendiki A, Wald LL, Adalsteinsson E. Accelerated diffusion spectrum imaging with compressed sensing using adaptive dictionaries. Magn Reson Med. 2012;68(6):1747-54.

10. Wang H, Black AJ, Zhu J, Stigen TW, Al-Qaisi MK, Netoff TI, Abosch A, Akkin T. Reconstructing micrometer-scale fiber pathways in the brain: multi-contrast optical coherence tomography based tractography. Neuroimage. 2011 Oct 15;58(4):984-92.

11. Grisot G, Jones R, Augustinack J, Boas D, Fischl B, Wang H, Yendiki A. Validation of high angular resolution diffusion MRI models in the human brain with PS-OCT. International Society for Magnetic Resonance in Medicine (ISMRM). 2017.

12. Aharon M, Elad M, Bruckstein A. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on signal processing. 2006 Nov 1;54(11):4311.