Tomography is the area of reconstructing objects from projections. In discrete tomography an object T we wish to reconstruct may be a set of cells of a multidimensional grid. We perform measurements of T , each one involving a projection that determines the number of cells in T on all lines parallel to the projection’s direction. Given a finite number of such measurements, we wish to reconstruc...

In this paper we prove several new stability results for the reconstruction of binary images from two projections. We consider an original image that is uniquely determined by its projections and possible reconstructions from slightly different projections. We show that for a given difference in the projections, the reconstruction can only be disjoint from the original image if the size of the ...

Discrete tomography (DT) is concerned with the tomographic reconstruction of images that consist of only a small number of grey levels. Recently, DART, a practical algorithm was introduced for discrete tomography, which was validated in the domain of X-ray computed and electron tomography. In this paper, DART is introduced for magnetic resonance imaging. Using simulation experiments, it is show...

Tomography deals with the reconstruction of the density distribution inside an unknown object from its projections in several directions. In Discrete tomography one focuses on the reconstruction of objects having a small, discrete set of density values. Using this prior knowledge in the reconstruction algorithm may vastly reduce the number of projections that is required to obtain high quality ...

Discrete tomography concerns the reconstruction of functions with a finite number of values from few projections. For a number of important real-world problems, this tomography problem involves thousands of variables. Applicability and performance of discrete tomography therefore largely depend on the criteria used for reconstruction and the optimization algorithm applied. From this viewpoint, ...

We developed a discrete tomography method for prostate implant reconstructions using only a limited number of X-ray projection images. A 3D voxel volume is reconstructed by back-projection and using distance maps generated from the projection images. The true seed locations are extracted from the voxel volume while false positive seeds are eliminated using a novel optimal geometry coverage mode...

Recent X-ray techniques allow for the first time to image small crystals – known as grains – deep inside of polycrystalline materials. This is of interest in materials science. Two important techniques are based on tomography principles related to discrete tomography. We give a short introduction to the basic reconstruction problems arising in this context. The focus is on revealing the mathema...