MPI reconstruction using Bessel functions

Abstract

This publication proposes for the first time a direct reconstruction technique based on weighted Bessel functions of first kind. As basis for the formulation the well-known Chebyshev reconstruction is used. By utilizing the Fourier transform of Chebyshev polynomials of second kind, which is nothing else than a weighted Bessel function of first kind, a new formulation which allows for reconstruction of the particle distribution in the Fourier domain is derived. This method comes with the benefit of allowing for a direct deconvolution in frequency domain. With numerical simulations we show the equivalence to the Chebyshev reconstruction and demonstrate different strategies to perform the deconvolution.

Int. J. Mag. Part. Imag. 6(2), Suppl. 1, 2020, Article ID: 2009017, DOI: 10.18416/IJMPI.2020.2009017