Universiteit Leiden

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Discrete tomography for integer-valued functions

Promotor: S.J. Edixhoven, Co-promotor: K.J. Batenburg

Arjen Stolk
15 juni 2011
Thesis in Leiden Repository

This thesis studies the reconstruction of integer-valued functions on subsets of the rectangular lattice in R^n, given the sums of function values over lines going through this subset. This problem is a relaxation of the well-studied discrete tomography problem of reconstructing binary images from counts of ones along straight lines. The relaxation has rich and interesting algebraic structure. Among other things, this leads to a classification of numerical relations between the line sums.