Title:Diffusionweighted magnetic resonance signal as a series of Hermite
functions
Abstract:Following a brief overview of the diffusionweighted (DW) magnetic resonance (MR) technique, a series representation of the DWMR signals
will be presented in terms of a complete set of orthogonal Hermite
functions. The basis possesses many interesting properties relevant to
DWMR, such as the ability to represent both the signal and its Fourier
transform; this property lends itself to a direct reconstruction of
ensemble average propagators. Moreover, the estimation problem is
linear, and the basis is capable of approximating even the most
complicated signal profiles one can encounter. The analytical
representation provided by the method is employed to directly estimate
several important microstructural characteristics of the specimen such
as its structural anisotropy and the moments of the underlying pore size
distribution.
