A novel convex relaxation for non-binary discrete tomography

• Verfasst von: Plier, Jan [VerfasserIn]
• Verfasst von: Swoboda, Paul [VerfasserIn]
• Verfasst von: Petra, Stefania [VerfasserIn]
• Titel: A novel convex relaxation for non-binary discrete tomography
• Verf.angabe: Jan Kuske, Paul Swoboda, Stefania Petra
• E-Jahr: 2017
• Jahr: 18 May 2017
• Umfang: 12 S.
• Fussnoten: Gesehen am 14.03.2018
• Titel Quelle: Enthalten in: Scale Space and Variational Methods in Computer Vision
• Ort Quelle: Cham : Springer, 2017
• Jahr Quelle: 2017
• Band/Heft Quelle: (2017), Seite 235-246
• ISBN Quelle: 978-3-319-58771-4
• DOI: doi:10.1007/978-3-319-58771-4_19
• Datenträger: Online-Ressource
• Dokumenttyp: Konferenzschrift
• Sprache: eng
• K10plus-PPN: 1571046984

Abstract

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art approaches that split the problem into a continuous reconstruction problem for the linear measurement constraints and a discrete labeling problem to enforce discrete-valued reconstructions, we propose a joint formulation that addresses both problems simultaneously, resulting in a tighter convex relaxation. For this purpose a constrained graphical model is set up and evaluated using a novel relaxation optimized by dual decomposition. We evaluate our approach experimentally and show superior solutions both mathematically (tighter relaxation) and experimentally in comparison to previously proposed relaxations.