A rounding theorem for unique binary tomographic reconstruction

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1 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)54-69
Numero di pagine16
RivistaDiscrete Applied Mathematics
Volume268
DOI
Stato di pubblicazionePubblicato - 2019

Keywords

  • Binary tomography
  • Discrete tomography
  • Lattice direction
  • Lattice grid
  • Minimum norm solution
  • Uniqueness of reconstruction

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