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# Single and Multiple Shell Sampling Design in dMRI Using Spherical code and Mixed Integer Linear Programming

* Corresponding author
BRIC - Biomedical Research Imaging Center [North Carolina]
Abstract : Sampling scheme is crucial in diffusion MRI data acquisition and reconstruction. A good sampling scheme can obtain good reconstruction results with less number of samples in diffusion q-space. It has been showed that for the diffusion data obtained from single shell (single b value), the uniform sampling scheme has good performance in a general case because it does not assume a preferred direction. In last decade, two kinds of uniform single shell sampling schemes are widely used in diffusion MRI field, i.e. the sphere tessellation and electrostatic energy minimization introduced in dMRI by Jones [1] However sphere tessellation cannot handle arbitrary number of samples, and electrostatic energy minimization lacks its physical meaning related to reconstructions in dMRI. It is still unclear that why electrostatic energy matters in diffusion data reconstruction? We hope the samples in sphere have large angular difference such that the "angular resolution" in reconstruction can be as large as possible, so mathematically a more natural way is to define a uniform sampling scheme $\{u_i\}$ such that the minimal angular difference can be as large as possible, which is essentially the Spherical Code (SC) problem [2]. Some optimal configurations for sphere $S^2$ for different number K have been collected in [3]. Although the solutions in [3] can be directly used in dMRI, they have two main limitations. 1) They are for single sphere, not for multi-shell schemes. 2) For real applications in dMRI, sometimes we need to find one or several sets of "uniform" schemes from a given set of sampling scheme, which is the "discretized" SC problem. In this paper, we propose a general Mixed Integer Linear Programming (MILP) framework to design "uniform" sampling schemes for both single and multi-shell dMRI. Although some recent works proposed to generalized electrostatic energy minimization uniform method to single/multi-shell multi-shell case sampling [4], to our scheme knowledge, this paper is the first work to design single/multi-shell sampling scheme using SC formulation.
Document type :
Conference papers
Domain :

https://hal.archives-ouvertes.fr/hal-01011892
Contributor : Jian Cheng Connect in order to contact the contributor
Submitted on : Friday, June 27, 2014 - 6:09:19 PM
Last modification on : Wednesday, August 21, 2019 - 10:22:07 AM
Long-term archiving on: : Saturday, September 27, 2014 - 10:40:45 AM

### File

sampling_ISMRM2014.pdf
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### Identifiers

• HAL Id : hal-01011892, version 1

### Citation

Jian Cheng, Pew-Thian Yap, Dinggang Shen. Single and Multiple Shell Sampling Design in dMRI Using Spherical code and Mixed Integer Linear Programming. ISMRM, May 2014, Italy. pp.2558. ⟨hal-01011892⟩

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