A semi-automatic algorithm for grey level estimation in tomography

Discrete tomography focuses on the reconstruction of images that contain only a few grey levels from their projections. By incorporating prior knowledge about the set of grey levels, the required number of projections can be reduced substantially. In practical applications, however, the number of grey levels is often known in advance, yet the actual grey level values are unknown. Moreover, it can be difficult to estimate these grey levels, particularly if only a small number of projections are available. In this paper, we propose a semi-automatic approach for grey level estimation that can be used as a preprocessing step before applying discrete tomography algorithms. After an initial, non-discrete reconstruction has been computed, the user first selects some regions that are likely to correspond with the respective grey levels. The fact that these regions should be constant in the original image is then used as prior knowledge in the grey level estimation algorithm. We present the results of a series of simulation experiments, demonstrating the accuracy and robustness of our approach.

Research highlights
► Discrete tomography enables image reconstruction from few projection images.
► To use discrete tomography, prior knowledge of the grey levels is required.
► This paper proposes an algorithm for estimating grey levels from the projections.
► The proposed algorithms is both robust and accurate.