title: Estimation of non-negative ODFs using the eigenvalue distribution of spherical functions.
abstract: Current methods in high angular resolution diffusion imaging (HARDI) estimate the probability density function of water diffusion as a continuous-valued orientation distribution function (ODF) on the sphere. However, such methods could produce an ODF with negative values, because they enforce non-negativity only at finitely many directions. In this paper, we propose to enforce non-negativity on the continuous domain by enforcing the positive semi-definiteness of Toeplitz-like matrices constructed from the spherical harmonic representation of the ODF. We study the distribution of the eigenvalues of these matrices and use it to derive an iterative semi-definite program that enforces non-negativity on the continuous domain. We illustrate the performance of our method and compare it to the state-of-the-art with experiments on synthetic and real data.
authors.affiliation: Center for Imaging Science, Johns Hopkins University, USA.
authors.forename: Evan
authors.initials: E
authors.lastname: Schwab
authors.forename: Bijan
authors.initials: B
authors.lastname: Afsari
authors.forename: René
authors.initials: R
authors.lastname: Vidal
mesh_terms: D000465:Algorithms; D001834:Body Water / Q000378:metabolism*; D001921:Brain / Q000033:anatomy & histology* / Q000378:metabolism*; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity