The JET neutron profile monitor ensures coverage of the neutron emissive region that enables tomographic reconstruction. However, due to the availability of only two projection angles and to the coarse sampling, tomography is a limited data set problem. A reconstruction method based on the maximum likelihood principle is developed for solving the reconstruction problem. A smoothing operator, defined as median filtering which uses a sliding window moving along magnetic contour lines, is used to compensate for the lack of experimental information. The method is tested on numerically simulated phantoms with shapes characteristic for this kind of tomography. Significant reconstructions of experimental data are reported.