Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code

Jian Cheng, Dinggang Shen, Pew Thian Yap

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

In diffusion MRI (dMRI), determining an appropriate sampling scheme is crucial for acquiring the maximal amount of information for data reconstruction and analysis using the minimal amount of time. For single-shell acquisition, uniform sampling without directional preference is usually favored. To achieve this, a commonly used approach is the Electrostatic Energy Minimization (EEM) method introduced in dMRI by Jones et al. However, the electrostatic energy formulation in EEM is not directly related to the goal of optimal sampling-scheme design, i.e., achieving large angular separation between sampling points. A mathematically more natural approach is to consider the Spherical Code (SC) formulation, which aims to achieve uniform sampling by maximizing the minimal angular difference between sampling points on the unit sphere. Although SC is well studied in the mathematical literature, its current formulation is limited to a single shell and is not applicable to multiple shells. Moreover, SC, or more precisely continuous SC (CSC), currently can only be applied on the continuous unit sphere and hence cannot be used in situations where one or several subsets of sampling points need to be determined from an existing sampling scheme. In this case, discrete SC (DSC) is required. In this paper, we propose novel DSC and CSC methods for designing uniform single-/multi-shell sampling schemes. The DSC and CSC formulations are solved respectively by Mixed Integer Linear Programming (MILP) and a gradient descent approach. A fast greedy incremental solution is also provided for both DSC and CSC. To our knowledge, this is the first work to use SC formulation for designing sampling schemes in dMRI. Experimental results indicate that our methods obtain larger angular separation and better rotational invariance than the generalized EEM (gEEM) method currently used in the Human Connectome Project (HCP).

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages281-288
Number of pages8
Volume8675 LNCS
EditionPART 3
ISBN (Print)9783319104423
DOIs
Publication statusPublished - 2014 Jan 1
Externally publishedYes
Event17th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2014 - Boston, MA, United States
Duration: 2014 Sep 142014 Sep 18

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 3
Volume8675 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other17th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2014
CountryUnited States
CityBoston, MA
Period14/9/1414/9/18

Fingerprint

Spherical Codes
Magnetic resonance imaging
Shell
Sampling
Electrostatics
Energy Minimization
Formulation
Unit Sphere
Mixed Integer Linear Programming
Gradient Descent
Invariance
Set theory
Linear programming

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Cheng, J., Shen, D., & Yap, P. T. (2014). Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (PART 3 ed., Vol. 8675 LNCS, pp. 281-288). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8675 LNCS, No. PART 3). Springer Verlag. https://doi.org/10.1007/978-3-319-10443-0_36

Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code. / Cheng, Jian; Shen, Dinggang; Yap, Pew Thian.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8675 LNCS PART 3. ed. Springer Verlag, 2014. p. 281-288 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8675 LNCS, No. PART 3).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Cheng, J, Shen, D & Yap, PT 2014, Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 3 edn, vol. 8675 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 3, vol. 8675 LNCS, Springer Verlag, pp. 281-288, 17th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2014, Boston, MA, United States, 14/9/14. https://doi.org/10.1007/978-3-319-10443-0_36
Cheng J, Shen D, Yap PT. Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 3 ed. Vol. 8675 LNCS. Springer Verlag. 2014. p. 281-288. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 3). https://doi.org/10.1007/978-3-319-10443-0_36
Cheng, Jian ; Shen, Dinggang ; Yap, Pew Thian. / Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8675 LNCS PART 3. ed. Springer Verlag, 2014. pp. 281-288 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 3).
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