Fast, model-free, analytical diffusion PDF profile estimation from the DWI signals

Abstract : How to estimate the diffusion Probability Density Function (PDF) from the q-space DWI signals is an open problem in diffusion MRI field. The diffusion PDF and the diffusion attenuation of dMRI signal is related by 3 dimensional Fourier transform. Diffusion Orientation Transform (DOT) [2] was proposed based on the assumption of the mono-exponential decay. Thanks to this assumption, PDF profile at a given radius R0 could be calculated analytically. However the estimated PDF is a low-pass filtered PDF. And this kind of low-pass filtering comes from the intrinsic modeling error [2], which is not a well defined filtering. Although DOT has been extended to multi-exponential model [2] and can reduce the modeling error dramatically, a nonlinear fitting needs to be performed for every voxel, which will limit its usefulness. Here we propose a model-free, linear, robust, analytical PDF profile reconstruction method which avoids the exponential or multi-exponential assumption.