### 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 language | English |
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Title of host publication | Applied and Numerical Harmonic Analysis |

Publisher | Springer International Publishing |

Pages | 333-366 |

Number of pages | 34 |

Edition | 9780817636142 |

DOIs | |

Publication status | Published - Jan 1 2007 |

### Publication series

Name | Applied and Numerical Harmonic Analysis |
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Number | 9780817636142 |

ISSN (Print) | 2296-5009 |

ISSN (Electronic) | 2296-5017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

TY - CHAP

T1 - Emission discrete tomography

AU - Barcucci, E.

AU - Frosini, A.

AU - Kuba, A.

AU - Nagy, A.

AU - Rinaldi, S.

AU - Šámal, M.

AU - Zopf, S.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - 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.

AB - 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.

KW - Binary matrix

KW - Generalize projection

KW - Renal pelvis

KW - Single photon emission compute tomography

KW - Vertical projection

UR - http://www.scopus.com/inward/record.url?scp=85047390409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047390409&partnerID=8YFLogxK

U2 - 10.1007/978-0-8176-4543-4_15

DO - 10.1007/978-0-8176-4543-4_15

M3 - Chapter

AN - SCOPUS:85047390409

T3 - Applied and Numerical Harmonic Analysis

SP - 333

EP - 366

BT - Applied and Numerical Harmonic Analysis

PB - Springer International Publishing

ER -