Mpi reconstruction using bessel functions

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.