Sets uniquely determined by projections on axes II Discrete case
Discrete Mathematics
Three-Dimensional Statistical Data Security Problems
SIAM Journal on Computing
On the computational complexity of reconstructing lattice sets from their x-rays
Discrete Mathematics
On the comptational complexity of determining polyatomic structures by X-rays
Theoretical Computer Science
Approximating Binary Images from Discrete X-Rays
SIAM Journal on Optimization
On the Reconstruction of Finite Lattice Sets from their X-Rays
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Stability in discrete tomography: some positive results
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Stability in Discrete Tomography: some positive results
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
On the stability of reconstructing lattice sets from x-rays along two directions
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Discrete tomography for inscribable lattice sets
Discrete Applied Mathematics
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The paper gives strong instability results for a basic reconstruction problem of discrete tomography, an area that is particularly motivated by demands from material sciences for the reconstruction of crystalline structures from images produced by quantitative high resolution transmission electron microscopy. In particular, we show that even extremely small changes in the data may lead to entirely different solutions. We will also give some indication of how one can possibly handle the ill-posedness of the reconstruction problem in practice.