title: Background and Mathematical Analysis of Diffusion MRI Methods.
abstract: The addition of a pair of magnetic field gradient pulses had initially provided the measurement of spin motion with nuclear magnetic resonance (NMR) techniques. In the adaptation of 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 diffusion weighted (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.
authors: Health Research, Arlington Innovation Center, Virginia Polytechnic Institute and State University, 900 N. Glebe Road, Arlington VA, 22203, USA.
authors: Alpay
authors: A
authors: Ozcan
authors: Kenneth H
authors: KH
authors: Wong
authors: Linda
authors: L
authors: Larson-Prior
authors: Zang-Hee
authors: ZH
authors: Cho
authors: Seong K
authors: SK
authors: Mun
keywords: Diffusion; Diffusion Weighted Imaging; Fourier Transform; Magnetic Resonance Imaging; Nuclear Magnetic Resonance
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