TY - JOUR
T1 - Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes
AU - Cheng, Jian
AU - Shen, Dinggang
AU - Yap, Pew Thian
AU - Basser, Peter J.
N1 - Funding Information:
Manuscript received June 9, 2017; revised August 17, 2017; accepted September 17, 2017. Date of publication September 26, 2017; date of current version December 29, 2017. This work was supported in part by the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development under Grant ZIA-HD000266, in part by NIH under Grant NS093842 and Grant EB022880. Data were provided in part by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and in part by the McDonnell Center for Systems Neuroscience at Washington University. (Corresponding authors: Jian Cheng; Pew-Thian Yap; Peter J. Basser.) J. Cheng and P.-J. Basser are with SQITS, NIBIB, NICHD, National Institutes of Health, Bethesda, MD 20892 USA (e-mail: jian.cheng@nih.gov; pjbasser@helix.nih.gov).
Publisher Copyright:
© 2017 IEEE.
PY - 2018/1
Y1 - 2018/1
N2 - In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The electrostatic energy minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multi-shell schemes, called generalized EEM (GEEM). GEEM has been successfully used in the human connectome project. However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called spherical code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to design single or multiple shell sampling schemes, but also discrete problems to uniformly extract sub-sampled schemes from an existing single or multiple shell scheme, and to order samples in an existing scheme. We propose five algorithms to solve the above problems, including an incremental SC (ISC), a sophisticated greedy algorithm called iterative maximum overlap construction (IMOC), an 1-Opt greedy method, a mixed integer linear programming method, and a constrained non-linear optimization method. To our knowledge, this is the first work to use the SC formulation for single or multiple shell sampling schemes in dMRI. Experimental results indicate that SC methods obtain larger angular separation and better rotational invariance than the state-of-the-art EEM and GEEM. The related codes and a tutorial have been released in DMRITool.
AB - In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The electrostatic energy minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multi-shell schemes, called generalized EEM (GEEM). GEEM has been successfully used in the human connectome project. However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called spherical code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to design single or multiple shell sampling schemes, but also discrete problems to uniformly extract sub-sampled schemes from an existing single or multiple shell scheme, and to order samples in an existing scheme. We propose five algorithms to solve the above problems, including an incremental SC (ISC), a sophisticated greedy algorithm called iterative maximum overlap construction (IMOC), an 1-Opt greedy method, a mixed integer linear programming method, and a constrained non-linear optimization method. To our knowledge, this is the first work to use the SC formulation for single or multiple shell sampling schemes in dMRI. Experimental results indicate that SC methods obtain larger angular separation and better rotational invariance than the state-of-the-art EEM and GEEM. The related codes and a tutorial have been released in DMRITool.
KW - Sampling
KW - diffusion MRI
KW - multiple shells
KW - q-space
KW - spherical codes
KW - uniform spherical sampling
UR - http://www.scopus.com/inward/record.url?scp=85030709350&partnerID=8YFLogxK
U2 - 10.1109/TMI.2017.2756072
DO - 10.1109/TMI.2017.2756072
M3 - Article
C2 - 28952937
AN - SCOPUS:85030709350
SN - 0278-0062
VL - 37
SP - 185
EP - 199
JO - IEEE Transactions on Medical Imaging
JF - IEEE Transactions on Medical Imaging
IS - 1
M1 - 8049360
ER -