### Abstract

This paper studies the classical tomographical problem of the reconstruction of a binary matrix from projections in presence of absorption. In particular, we consider two projections along the horizontal and vertical directions and the mathematically interesting case of the absorption coefficient β_{0} = frac(1 + sqrt(5), 2). After proving some theoretical results on the switching components, we furnish a fast algorithm for solving the reconstruction problem from the horizontal and vertical absorbed projections. As a significative remark, we obtain also the solution of the related uniqueness problem.

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

Pages (from-to) | 347-363 |

Number of pages | 17 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 20 |

DOIs | |

Publication status | Published - Jul 1 2005 |

### Fingerprint

### Keywords

- absorbed projections
- Discrete tomography
- polynomial time algorithm
- reconstruction problem

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Electronic Notes in Discrete Mathematics*,

*20*, 347-363. https://doi.org/10.1016/j.endm.2005.05.073

**An efficient algorithm for reconstructing binary matrices from horizontal and vertical absorbed projections.** / Frosini, A.; Rinaldi, S.; Barcucci, E.; Kuba, A.

Research output: Contribution to journal › Article

*Electronic Notes in Discrete Mathematics*, vol. 20, pp. 347-363. https://doi.org/10.1016/j.endm.2005.05.073

}

TY - JOUR

T1 - An efficient algorithm for reconstructing binary matrices from horizontal and vertical absorbed projections

AU - Frosini, A.

AU - Rinaldi, S.

AU - Barcucci, E.

AU - Kuba, A.

PY - 2005/7/1

Y1 - 2005/7/1

N2 - This paper studies the classical tomographical problem of the reconstruction of a binary matrix from projections in presence of absorption. In particular, we consider two projections along the horizontal and vertical directions and the mathematically interesting case of the absorption coefficient β0 = frac(1 + sqrt(5), 2). After proving some theoretical results on the switching components, we furnish a fast algorithm for solving the reconstruction problem from the horizontal and vertical absorbed projections. As a significative remark, we obtain also the solution of the related uniqueness problem.

AB - This paper studies the classical tomographical problem of the reconstruction of a binary matrix from projections in presence of absorption. In particular, we consider two projections along the horizontal and vertical directions and the mathematically interesting case of the absorption coefficient β0 = frac(1 + sqrt(5), 2). After proving some theoretical results on the switching components, we furnish a fast algorithm for solving the reconstruction problem from the horizontal and vertical absorbed projections. As a significative remark, we obtain also the solution of the related uniqueness problem.

KW - absorbed projections

KW - Discrete tomography

KW - polynomial time algorithm

KW - reconstruction problem

UR - http://www.scopus.com/inward/record.url?scp=34247129214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247129214&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2005.05.073

DO - 10.1016/j.endm.2005.05.073

M3 - Article

AN - SCOPUS:34247129214

VL - 20

SP - 347

EP - 363

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -