### Abstract

The problem of reconstructing a measurable plane set from its two generalized projections is considered. It means that the projections contain also the effect of a known modification given in the whole plane. This is a more general case than that of a constant absorption within a given material. Via a suitable mapping, this generalized problem can be transformed into the solved case of the classical (non-absorbed and non-generalized) projections, giving a theorem about the characterization of unique, non-unique, and inconsistent projections analogous to Lorentz' theorem. The connection between uniqueness and the existence of so-called generalized switching components is discussed.

Original language | English |
---|---|

Pages (from-to) | 47-66 |

Number of pages | 20 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 20 |

DOIs | |

Publication status | Published - Jul 1 2005 |

### Fingerprint

### Keywords

- absorption
- Discrete tomography
- emission discrete tomography
- Lorentz' theorem
- projection
- switching component

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

**Reconstruction of measurable sets from two generalized projections.** / Zopf, Steffen; Kuba, A.

Research output: Contribution to journal › Article

*Electronic Notes in Discrete Mathematics*, vol. 20, pp. 47-66. https://doi.org/10.1016/j.endm.2005.04.003

}

TY - JOUR

T1 - Reconstruction of measurable sets from two generalized projections

AU - Zopf, Steffen

AU - Kuba, A.

PY - 2005/7/1

Y1 - 2005/7/1

N2 - The problem of reconstructing a measurable plane set from its two generalized projections is considered. It means that the projections contain also the effect of a known modification given in the whole plane. This is a more general case than that of a constant absorption within a given material. Via a suitable mapping, this generalized problem can be transformed into the solved case of the classical (non-absorbed and non-generalized) projections, giving a theorem about the characterization of unique, non-unique, and inconsistent projections analogous to Lorentz' theorem. The connection between uniqueness and the existence of so-called generalized switching components is discussed.

AB - The problem of reconstructing a measurable plane set from its two generalized projections is considered. It means that the projections contain also the effect of a known modification given in the whole plane. This is a more general case than that of a constant absorption within a given material. Via a suitable mapping, this generalized problem can be transformed into the solved case of the classical (non-absorbed and non-generalized) projections, giving a theorem about the characterization of unique, non-unique, and inconsistent projections analogous to Lorentz' theorem. The connection between uniqueness and the existence of so-called generalized switching components is discussed.

KW - absorption

KW - Discrete tomography

KW - emission discrete tomography

KW - Lorentz' theorem

KW - projection

KW - switching component

UR - http://www.scopus.com/inward/record.url?scp=34247104669&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247104669&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2005.04.003

DO - 10.1016/j.endm.2005.04.003

M3 - Article

AN - SCOPUS:34247104669

VL - 20

SP - 47

EP - 66

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -