Non-negative spherical deconvolution (NNSD) for fiber orientation distribution function estimation

Jian Cheng, Rachid Deriche, Tianzi Jiang, Dinggang Shen, Pew Thian Yap

Research output: Contribution to journalArticlepeer-review


In diffusion Magnetic Resonance Imaging (dMRI), Spherical Deconvolution (SD) is a commonly used approach for estimating the fiber Orientation Distribution Function (fODF). As a Probability Density Function (PDF) that characterizes the distribution of fiber orientations, the fODF is expected to be non-negative and to integrate to unity on the continuous unit sphere S2. However, many existing approaches, despite using continuous representation such as Spherical Harmonics (SH), impose non-negativity only on discretized points of S2. Therefore, nonnegativity is not guaranteed on the whole S2. Existing approaches are also known to exhibit false positive fODF peaks, especially in regions with low anisotropy, causing an over-estimation of the number of fascicles that traverse each voxel. This paper proposes a novel approach, called Non-Negative SD (NNSD), to overcome the above limitations. NNSD offers the following advantages. First, NNSD is the first SH based method that guarantees non-negativity of the fODF throughout the unit sphere. Second, unlike approaches such as Maximum Entropy SD (MESD), Cartesian Tensor Fiber Orientation Distribution (CT-FOD), and discrete representation based SD (DR-SD) techniques, the SH representation allows closed form of spherical integration, efficient computation in a low dimensional space resided by the SH coefficients, and accurate peak detection on the continuous domain defined by the unit sphere. Third, NNSD is significantly less susceptible to producing false positive peaks in regions with low anisotropy. Evaluations of NNSD in comparison with Constrained SD (CSD), MESD, and DR-SD (implemented using L1-regularized least-squares with non-negative constraint), indicate that NNSD yields improved performance for both synthetic and real data. The performance gain is especially prominent for high resolution .1:25mm/3 data.

Original languageEnglish
Pages (from-to)81-93
Number of pages13
JournalMathematics and Visualization
Publication statusPublished - 2014
Externally publishedYes

ASJC Scopus subject areas

  • Modelling and Simulation
  • Geometry and Topology
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


Dive into the research topics of 'Non-negative spherical deconvolution (NNSD) for fiber orientation distribution function estimation'. Together they form a unique fingerprint.

Cite this