For continuous tomography Helgason and Ludwig developed consistency conditions. They were used by others to overcome defects in the measurements. In this paper we introduce a consistency criterion for discrete tomography. We indicate how the consistency criterion can be used to overcome defects in measurements.
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Discrete tomography deals with tomographic reconstruction of greyscale images for which the set of possible grey levels is discrete and small. Here, we develop a discrete approximate reconstruction algorithm. Our algorithm computes an image that has only grey values belonging to a given finite set. It also guarantees that the difference between the given projections and the projections of the reconstructed discrete image is bounded. The bound, which is computable, is independent of the image size. We present reconstruction experiments for a range of phantom images and a varying number of grey values.
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