Uniqueness Results for Grey Scale Digital Images

Issue title: Special Issue on Tomography and Neuroscience

Guest editors: Sara Brunetti, Paolo Dulio, Andrea Frosini and Grzegorz Rozenberg

Article type: Research Article

Authors: Brunetti, Sara^{a; *} | Dulio, Paolo^b | Peri, Carla^c

Affiliations: [a] Dipartimento di Ingegneria dell’Informazione, e Scienze Matematiche, Via Roma 56, 50129 Siena, Italy. sara.brunetti@unisi.it | [b] Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci 32 I-20133 Milano, Italy. paolo.dulio@polimi.it | [c] Universitá Cattolica del Sacro Cuore, Via Emilia Parmense 84, 29122 Piacenza, Italy. carla.peri@unicatt.it

Correspondence: [*] Address for correspondence: Dipartimento di Ingegneria dell’Informazione, e Scienze Matematiche, Via Roma 56, 50129 Siena, Italy

Abstract: We address the problem of reconstructing digital images with finitely many grey levels from the knowledge of their X-rays in a given finite set of lattice directions. The main result of the paper provides sets of 2p (p ≥ 3) lattice directions which uniquely determine images with p grey levels, contained in a finite lattice grid. This extends previous uniqueness results for binary images.

DOI: 10.3233/FI-2020-1902

Journal: Fundamenta Informaticae, vol. 172, no. 2, pp. 221-238, 2020