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Discrete tomography (DT) is a new technique to reconstruct discrete images from their projections (like neutron images). The reconstruction methods in DT are different from the conventional ones, because the created images may contain only a few numbers of given discrete values. One of the main reasons to apply DT is that hopefully we need only a few numbers of projections. In many applications we have a situation where we know the material components of the object to be studied, that is, we know the discrete values of the image to be reconstructed. Using discreteness and some a priori information we can apply several DT methods in neutron imaging. Most of the DT reconstruction methods are reducing the problem to an optimization task. We tried two such methods on software and physical phantoms. In these experiments we investigated the effects of the following parameters: number of projections, noise levels, and complexity of the object to be reconstructed. We also developed a software system, called DIRECT, for testing different DT methods, to compare them and to present the reconstructed objects.