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Reconstructing (0,1)-matrices from projections using integer programming

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Abstract

We study the problem of reconstructing (0,1)-matrices based on projections along a small number of directions. This discrete inverse problem is generally hard to solve for more than 3 projection directions. Building on previous work by the authors, we give a problem formulation with the objective of finding matrices with the maximal number of neighboring ones. A solution approach based on variable splitting and the use of subgradient optimization is given. Further, computational results are given for some structured instances. Optimal solutions are found for instances with up to 10,000 binary variables.

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Authors and Affiliations

  1. Centre of Mathematics for Application and Department of Informatics, University of Oslo, PO Box 1053, Blindern, 0316, Oslo, Norway

    Geir Dahl & Truls Flatberg

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  1. Geir Dahl
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  2. Truls Flatberg
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Correspondence to Truls Flatberg.

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Dahl, G., Flatberg, T. Reconstructing (0,1)-matrices from projections using integer programming. Comput Optim Appl 42, 141–154 (2009). https://doi.org/10.1007/s10589-007-9116-y

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  • DOI: https://doi.org/10.1007/s10589-007-9116-y

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