A 4D hyperspherical interpretation of q-space

A. Pasha Hosseinbor, Moo K. Chung, Yu Chien Wu, Barbara B. Bendlin, Andrew L. Alexander

Research output: Contribution to journalArticle

2 Scopus citations


3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space.

Original languageEnglish (US)
Pages (from-to)15-28
Number of pages14
JournalMedical Image Analysis
Issue number1
StatePublished - Apr 1 2015


  • Diffusion MRI
  • Diffusion propagator
  • Hyperspherical harmonics
  • ODF
  • Q-Space indices

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging
  • Computer Vision and Pattern Recognition
  • Health Informatics
  • Computer Graphics and Computer-Aided Design

Fingerprint Dive into the research topics of 'A 4D hyperspherical interpretation of q-space'. Together they form a unique fingerprint.

  • Cite this

    Pasha Hosseinbor, A., Chung, M. K., Wu, Y. C., Bendlin, B. B., & Alexander, A. L. (2015). A 4D hyperspherical interpretation of q-space. Medical Image Analysis, 21(1), 15-28. https://doi.org/10.1016/j.media.2014.11.013