Some families of generating functions for the multiple orthogonal polynomials associated with modified Bessel K-functions

AbstractThe main object of this paper is to derive several substantially more general families of bilinear, bilateral, and mixed multilateral finite-series relationships and generating functions for the multiple orthogonal polynomials associated with the modified Bessel K-functions also known as Macdonald functions. Some special cases of the above statements are also given

Efficient Computation of PDF-Based Characteristics from Diffusion MR Signal

International audienceWe present a general method for the computation of PDF-based characteristics of the tissue micro-architecture in MR imaging. The approach relies on the approximation of the MR signal by a series expansion based on Spherical Harmonics and Laguerre-Gaussian functions, followed by a simple projection step that is efficiently done in a finite dimensional space. The resulting algorithm is generic, flexible and is able to compute a large set of useful characteristics of the local tissues structure. We illustrate the effectiveness of this approach by showing results on synthetic and real MR datasets acquired in a clinical time-frame