4 materials scene reconstructions from line Mojette projections

The binary image reconstruction has been adressed for many years by discrete tomography.The Dirac Mojette transform allows for a more general framework with any kind of values and any number of projections. This paper mainly adress the 4 materials scene reconstrction by the line Mojette algorithm.The line Mojette uses the characteristics that the scene under reconstruction is composed of 4 material values. Since a projection line might contain a unique material value, then the pixels of this line can be back-projected directly with the unique material value. The inverse line Mojette can always solve more than one pixel at a time contrarily to the Dirac Mojette inversion. The constraint solver as the second part of the algorithm can make the reconstruction continue while there is no correspondence bin can be used. Under the Farey-Haros series and the Stern-Brocot tree projection sets, the experimental results demonstrated that line Mojette algorithm can complete the 4 materials scene reconstruction with the limited projection sets, which the Katz's criterion is far to be checked. (C) 2018 The Authors. Published by Elsevier B.V.