A new model for diffusion weighted MRI: complete Fourier direct MRI.

The diffusion weighted MR signal is modeled using particle methods. The model shows that the signal is the Fourier transform of the distribution function of the number of spins at the initial time at a given position with a given displacement integral value. The distribution function is computed via Fourier transform steps that keep the Hermitian property of the signal in order to guarantee that the distribution function is real valued. The function, which depicts the tissue microstructure 'as it is' without being tied to any expansions, transformations and assumptions such as Markovian property or symmetry about the spin motions, is displayed using isosurfaces overlayed on the spin density map for a fixed baboon brain sample.