A Novel Convex Relaxation for Non-binary Discrete Tomography

  • Jan KuskeEmail author
  • Paul Swoboda
  • Stefania Petra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)


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.


Linear Programming Relaxation Convex Relaxation Bundle Method High Order Factor Restricted Isometry Property 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.MIG, Institute of Applied MathematicsHeidelberg UniversityHeidelbergGermany
  2. 2.Institute of Science and Technology (IST) AustriaKlosterneuburgAustria

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