Diffusion-weighted magnetic resonance signal as a series of Hermite functions
Following a brief overview of the diffusion-weighted (DW) magnetic resonance (MR) technique, a series representation of the DW-MR signals will be presented in terms of a complete set of orthogonal Hermite functions. The basis possesses many interesting properties relevant to DW-MR, 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.