Evren Ozarslan1, Cheng Guan Koay1, Timothy M. Shepherd2, Stephen J. Blackband3, Peter J. Basser1
1STBB / NICHD, National Institutes of Health, Bethesda, MD, USA; 2University of California, San Francisco; 3University of Florida
We present an analytical representation of the three-dimensional q-space signal as a series of eigenfunctions of the 3D simple harmonic oscillator operator in spherical coordinates. The estimation problem lends itself naturally to a convex quadratic programming problem where we impose inequality constraints ensuring the positivity of the probabilities. The reconstruction of the average propagator is immediate once the estimation is performed. The results on human hippocampus data suggest that the technique is practical and robust.