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Background and mathematical analysis of diffusion MRI methods

The addition of a pair of magnetic field gradient pulses had initially enabled the measurement of spin motion to nuclear magnetic resonance (NMR) experiments. In the adaptation of diffusion weighted (DW)‐NMR techniques to magnetic resonance imaging (MRI), the taxonomy of mathematical models is divided in two categories: model matching and spectral methods. In this review, the methods are summarized starting from early DW NMR models followed up with their adaptation to DW MRI. Finally, a newly introduced Fourier analysis based unifying theory, so‐called Complete Fourier Direct MRI, is included to explain the mechanisms of existing methods. © 2012 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 22, 44–52, 2012