Skip to Main content Skip to Navigation
Theses

Programmation mathématique en tomographie discrète

Abstract : The tomographic imaging problem deals with reconstructing an objectfrom a data called a projections and collected by illuminating the objectfrom many different directions. A projection means the information derivedfrom the transmitted energies, when an object is illuminated from a particularangle. The solution to the problem of how to reconstruct an object fromits projections dates to 1917 by Radon. The tomographic reconstructingis applicable in many interesting contexts such as nondestructive testing,image processing, electron microscopy, data security, industrial tomographyand material sciences.Discete tomography (DT) deals with the reconstruction of discret objectfrom limited number of projections. The projections are the sums along fewangles of the object to be reconstruct. One of the main problems in DTis the reconstruction of binary matrices from two projections. In general,the reconstruction of binary matrices from a small number of projections isundetermined and the number of solutions can be very large. Moreover, theprojections data and the prior knowledge about the object to reconstructare not sufficient to determine a unique solution. So DT is usually reducedto an optimization problem to select the best solution in a certain sense.In this thesis, we deal with the tomographic reconstruction of binaryand colored images. In particular, research objectives are to derive thecombinatorial optimization techniques in discrete tomography problems.
Document type :
Theses
Complete list of metadata

Cited literature [50 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00957445
Contributor : Abes Star :  Contact
Submitted on : Monday, March 10, 2014 - 2:18:14 PM
Last modification on : Saturday, December 21, 2019 - 3:55:07 AM
Long-term archiving on: : Tuesday, June 10, 2014 - 12:10:24 PM

File

ThA_se_TLIG_-_Ghassen.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-00957445, version 1

Collections

Citation

Ghassen Tlig. Programmation mathématique en tomographie discrète. Traitement des images [eess.IV]. Conservatoire national des arts et metiers - CNAM; Université Tunis El Manar. Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis (Tunisie), 2013. Français. ⟨NNT : 2013CNAM0886⟩. ⟨tel-00957445⟩

Share

Metrics

Record views

730

Files downloads

1647