Binary tomography by iterating linear programs

Weber, Stefan ; Schnörr, Christoph ; Schüle, Thomas ; Hornegger, Joachim

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URN: urn:nbn:de:bsz:180-madoc-18064
Document Type: Working paper
Year of publication: 2004
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Subject headings (SWD): Diskrete Tomographie , Lineare Optimierung , Kombinatorische Optimierung
Keywords (English): Discrete Tomography , Combinatorial Optimization , Linear Programming , D.C. Programming
Abstract: A novel approach to the reconstruction problem of binary tomography from a small number of X-ray projections is presented. Based on our previous work, we adopt a linear programming relaxation of this combinatorial problem which includes an objective function for the reconstruction, the approximation of a smoothness prior enforcing spatially homogeneous solutions, and the projection constraints. We supplement this problem with an unbiased concave functional in order to gradually enforce binary minimizers. Application of a primal-dual subgradient iteration for optimizing this enlarged problem amounts to solve a sequence of linear programs, where the objective function changes in each step, yielding a sequence of solutions which provably converges.
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