Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using\r\nhigher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex\r\nADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the\r\nensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors\r\nwere developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF),\r\nsince it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel\r\nclosed-formapproximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since\r\nthe solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes\r\nthe effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms.We\r\ndemonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.
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