  In this work we investigate numerically the reconstruction approach proposed
in Goncharov, Novikov, 2016, for weighted ray transforms (weighted Radon
transforms along oriented straight lines) in 3D. In particular, the approach is
based on a geometric reduction of the data modeled by weighted ray transforms
to new data modeled by weighted Radon transforms along two-dimensional planes
in 3D. Such reduction could be seen as a preprocessing procedure which could be
further completed by any preferred reconstruction algorithm. In a series of
numerical tests on modelized and real SPECT (single photon emission computed
tomography) data we demonstrate that such procedure can significantly reduce
the impact of noise on reconstructions.
