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

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 Jian Cheng University of North Carolina at Chapel Hill, e-mail: [email protected] Rachid Deriche INRIA Sophia Antipolis, e-mail: [email protected] Tianzi Jiang Institute of Automation, Chinese Academy of Sciences, e-mail: [email protected] Dinggang Shen University of North Carolina at Chapel Hill, e-mail: [email protected] Pew-Thian Yap University of North Carolina at Chapel Hill, e-mail: [email protected]