Multi-tissue decomposition of diffusion MRI signals via ℓ0 sparse-group estimation

Pew Thian Yap, Yong Zhang, Dinggang Shen

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


Sparse estimation techniques are widely utilized in diffusion magnetic resonance imaging (DMRI). In this paper, we present an algorithm for solving the ℓ0 sparse-group estimation problem and apply it to the tissue signal separation problem in DMRI. Our algorithm solves the ℓ0 problem directly, unlike existing approaches that often seek to solve its relaxed approximations. We include the mathematical proofs showing that the algorithm will converge to a solution satisfying the first-order optimality condition within a finite number of iterations. We apply this algorithm to DMRI data to tease apart signal contributions from white matter, gray matter, and cerebrospinal fluid with the aim of improving the estimation of the fiber orientation distribution function (FODF). Unlike spherical deconvolution approaches that assume an invariant fiber response function (RF), our approach utilizes an RF group to span the signal subspace of each tissue type, allowing greater flexibility in accounting for possible variations of the RF throughout space and within each voxel. Our ℓ0 algorithm allows for the natural groupings of the RFs to be considered during signal decomposition. Experimental results confirm that our method yields estimates of FODFs and volume fractions of tissue compartments with improved robustness and accuracy. Our ℓ0 algorithm is general and can be applied to sparse estimation problems beyond the scope of this paper.

Original languageEnglish
Article number7505644
Pages (from-to)4340-4353
Number of pages14
JournalIEEE Transactions on Image Processing
Issue number9
Publication statusPublished - 2016 Sept


  • Diffusion MRI
  • fiber orientation distribution function (FODF)
  • sparse-group approximation
  • ℓ regularization

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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