On the reconstruction of finite lattice sets from their X-rays

Peter Gritzmann

doi:10.1007/BFb0024827

On the reconstruction of finite lattice sets from their X-rays

Peter Gritzmann

Chair of Geometry

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

17 Scopus citations

Abstract

We study various theoretical and algorithmic aspects of inverse problems in discrete tomography that are 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 discuss questions related to the ill-posedness of the problem, determine the computational complexity of the basic underlying tasks and indicate algorithmic approaches in the presence of XXX-hardness.

Original language	English
Title of host publication	Discrete Geometry for Computer Imagery - 7th International Workshop, DGCI 1997, Proceedings
Editors	Ehoud Ahronovitz, Christophe Fiorio
Publisher	Springer Verlag
Pages	19-32
Number of pages	14
ISBN (Print)	3540638849, 9783540638841
DOIs	https://doi.org/10.1007/BFb0024827
State	Published - 1997
Event	7th International Workshop on Discrete Geometry for Computer Imagery, DGCI 1997 - Montpellier, France Duration: 3 Dec 1997 → 5 Dec 1997

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1347
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th International Workshop on Discrete Geometry for Computer Imagery, DGCI 1997
Country/Territory	France
City	Montpellier
Period	3/12/97 → 5/12/97

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10.1007/BFb0024827

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Gritzmann, P. (1997). On the reconstruction of finite lattice sets from their X-rays. In E. Ahronovitz, & C. Fiorio (Eds.), Discrete Geometry for Computer Imagery - 7th International Workshop, DGCI 1997, Proceedings (pp. 19-32). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1347). Springer Verlag. https://doi.org/10.1007/BFb0024827

Gritzmann, Peter. / On the reconstruction of finite lattice sets from their X-rays. Discrete Geometry for Computer Imagery - 7th International Workshop, DGCI 1997, Proceedings. editor / Ehoud Ahronovitz ; Christophe Fiorio. Springer Verlag, 1997. pp. 19-32 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "On the reconstruction of finite lattice sets from their X-rays",

abstract = "We study various theoretical and algorithmic aspects of inverse problems in discrete tomography that are 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 discuss questions related to the ill-posedness of the problem, determine the computational complexity of the basic underlying tasks and indicate algorithmic approaches in the presence of XXX-hardness.",

author = "Peter Gritzmann",

note = "Publisher Copyright: {\textcopyright} Springer-Vertag Berlin Heidelberg 1997.; 7th International Workshop on Discrete Geometry for Computer Imagery, DGCI 1997 ; Conference date: 03-12-1997 Through 05-12-1997",

year = "1997",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Gritzmann, P 1997, On the reconstruction of finite lattice sets from their X-rays. in E Ahronovitz & C Fiorio (eds), Discrete Geometry for Computer Imagery - 7th International Workshop, DGCI 1997, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1347, Springer Verlag, pp. 19-32, 7th International Workshop on Discrete Geometry for Computer Imagery, DGCI 1997, Montpellier, France, 3/12/97. https://doi.org/10.1007/BFb0024827

On the reconstruction of finite lattice sets from their X-rays. / Gritzmann, Peter.
Discrete Geometry for Computer Imagery - 7th International Workshop, DGCI 1997, Proceedings. ed. / Ehoud Ahronovitz; Christophe Fiorio. Springer Verlag, 1997. p. 19-32 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1347).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Gritzmann P. On the reconstruction of finite lattice sets from their X-rays. In Ahronovitz E, Fiorio C, editors, Discrete Geometry for Computer Imagery - 7th International Workshop, DGCI 1997, Proceedings. Springer Verlag. 1997. p. 19-32. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/BFb0024827

On the reconstruction of finite lattice sets from their X-rays

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