Inhaltszusammenfassung

The present paper deals with the computational complexity of the discrete inverse problem of reconstructing finite point sets and more general functionals with finite support that are accessible only through some of the values of their discrete Radon transform. It turns out that this task behaves quite differently from its well-studied companion problem involving 1-dimensional X-rays. Concentrating on the case of coordinate hyperplanes in R-d and on functionals psi : Z(d) --> D with D is an e...The present paper deals with the computational complexity of the discrete inverse problem of reconstructing finite point sets and more general functionals with finite support that are accessible only through some of the values of their discrete Radon transform. It turns out that this task behaves quite differently from its well-studied companion problem involving 1-dimensional X-rays. Concentrating on the case of coordinate hyperplanes in R-d and on functionals psi : Z(d) --> D with D is an element of {{0, 1,...,r}, N-0} for some arbitrary but fixed r, we show in particular that the problem can be solved in polynomial time if information is available for m such hyperplanes when m less than or equal to d - 1 but is NP-hard for m = d and D = {0, 1,...,r}. However, for D = N-0, a case that is relevant in the context of contingency tables, the problem is still in P. Similar results are given for the task of determining the uniqueness of a given solution and for a related counting problem. (C) 2002 Elsevier Science B.V. All rights reserved. » weiterlesen» einklappen

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