Discrete tomography deals with the reconstruction of images from projections collected along a few given directions. Different approaches can be considered, according to different models. In this paper we adopt the grid model, where pixels are lattice points with integer coordinates, X-rays are discrete lattice lines, and projections are obtained by counting the number of lattice points intercepted by X-rays taken in the assigned directions. We move from a theoretical result that allows uniqueness of reconstruction in the grid with just four suitably selected X-ray directions. In this framework, the structure of the allowed ghosts is studied and described. This leads to a new result, stating that the unique binary solution can be explicitly and exactly retrieved from the minimum Euclidean norm solution by means of a rounding method based on some special entries, which are precisely determined. A corresponding iterative algorithm has been implemented, and tested on a few phantoms having different characteristics and structure.

Dulio, P., Pagani, S. M. C., A rounding theorem for unique binary tomographic reconstruction, <<DISCRETE APPLIED MATHEMATICS>>, 2019; 268 (N/A): 54-69. [doi:10.1016/j.dam.2019.05.005] [http://hdl.handle.net/10807/142463]

A rounding theorem for unique binary tomographic reconstruction

Pagani, Silvia M. C.
2019

Abstract

Discrete tomography deals with the reconstruction of images from projections collected along a few given directions. Different approaches can be considered, according to different models. In this paper we adopt the grid model, where pixels are lattice points with integer coordinates, X-rays are discrete lattice lines, and projections are obtained by counting the number of lattice points intercepted by X-rays taken in the assigned directions. We move from a theoretical result that allows uniqueness of reconstruction in the grid with just four suitably selected X-ray directions. In this framework, the structure of the allowed ghosts is studied and described. This leads to a new result, stating that the unique binary solution can be explicitly and exactly retrieved from the minimum Euclidean norm solution by means of a rounding method based on some special entries, which are precisely determined. A corresponding iterative algorithm has been implemented, and tested on a few phantoms having different characteristics and structure.
Inglese
Dulio, P., Pagani, S. M. C., A rounding theorem for unique binary tomographic reconstruction, <<DISCRETE APPLIED MATHEMATICS>>, 2019; 268 (N/A): 54-69. [doi:10.1016/j.dam.2019.05.005] [http://hdl.handle.net/10807/142463]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/142463
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 3
social impact