Non-negative Spherical Deconvolution (NNSD) for Fiber Orientation Distribution Function Estimation

  • Jian ChengEmail author
  • Rachid Deriche
  • Tianzi Jiang
  • Dinggang Shen
  • Pew-Thian YapEmail author
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


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 \({\mathbb{S}}^{2}\). However, many existing approaches, despite using continuous representation such as Spherical Harmonics (SH), impose non-negativity only on discretized points of \({\mathbb{S}}^{2}\). Therefore, non-negativity is not guaranteed on the whole \({\mathbb{S}}^{2}\). 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 \({(1.25\,\text{mm})}^{3}\) data.


Diffusion Tensor Image Spherical Harmonics Success Ratio Spherical Harmonics Coefficient Spurious Peak 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.University of North Carolina at Chapel HillChapel HillUSA
  2. 2.INRIA Sophia AntipolisValbonneFrance
  3. 3.Institute of AutomationChinese Academy of SciencesBeijingChina

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