Emission discrete tomography

E. Barcucci, A. Frosini, A. Kuba, A. Nagy, S. Rinaldi, M. Šámal, S. Zopf

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Three problems of emission discrete tomography (EDT) are presented. The first problem is the reconstruction of measurable plane sets from two absorbed projections. It is shown that Lorentz theorems can be generalized to this case. The second is the reconstruction of binary matrices from their absorbed row and columns sums if the absorption coefficient is μ0 = log((1+v/5)/2). It is proved that the reconstruction in this case can be done in polynomial time. Finally, a possible application of EDT in single photon emission computed tomography (SPECT) is presented: Dynamic structures are reconstructed after factor analysis.

Original languageEnglish
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages333-366
Number of pages34
Edition9780817636142
DOIs
Publication statusPublished - Jan 1 2007

Publication series

NameApplied and Numerical Harmonic Analysis
Number9780817636142
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Fingerprint

Discrete Tomography
Tomography
Single photon emission computed tomography
Factor analysis
Absorption Coefficient
Computed Tomography
Polynomials
Factor Analysis
Polynomial time
Photon
Projection
Binary
Theorem

Keywords

  • Binary matrix
  • Generalize projection
  • Renal pelvis
  • Single photon emission compute tomography
  • Vertical projection

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Barcucci, E., Frosini, A., Kuba, A., Nagy, A., Rinaldi, S., Šámal, M., & Zopf, S. (2007). Emission discrete tomography. In Applied and Numerical Harmonic Analysis (9780817636142 ed., pp. 333-366). (Applied and Numerical Harmonic Analysis; No. 9780817636142). Springer International Publishing. https://doi.org/10.1007/978-0-8176-4543-4_15

Emission discrete tomography. / Barcucci, E.; Frosini, A.; Kuba, A.; Nagy, A.; Rinaldi, S.; Šámal, M.; Zopf, S.

Applied and Numerical Harmonic Analysis. 9780817636142. ed. Springer International Publishing, 2007. p. 333-366 (Applied and Numerical Harmonic Analysis; No. 9780817636142).

Research output: Chapter in Book/Report/Conference proceedingChapter

Barcucci, E, Frosini, A, Kuba, A, Nagy, A, Rinaldi, S, Šámal, M & Zopf, S 2007, Emission discrete tomography. in Applied and Numerical Harmonic Analysis. 9780817636142 edn, Applied and Numerical Harmonic Analysis, no. 9780817636142, Springer International Publishing, pp. 333-366. https://doi.org/10.1007/978-0-8176-4543-4_15
Barcucci E, Frosini A, Kuba A, Nagy A, Rinaldi S, Šámal M et al. Emission discrete tomography. In Applied and Numerical Harmonic Analysis. 9780817636142 ed. Springer International Publishing. 2007. p. 333-366. (Applied and Numerical Harmonic Analysis; 9780817636142). https://doi.org/10.1007/978-0-8176-4543-4_15
Barcucci, E. ; Frosini, A. ; Kuba, A. ; Nagy, A. ; Rinaldi, S. ; Šámal, M. ; Zopf, S. / Emission discrete tomography. Applied and Numerical Harmonic Analysis. 9780817636142. ed. Springer International Publishing, 2007. pp. 333-366 (Applied and Numerical Harmonic Analysis; 9780817636142).
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