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

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

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Article ID: iaor200922521
Country: United States
Volume: 42
Issue: 1
Start Page Number: 141
End Page Number: 154
Publication Date: Jan 2009
Journal: Computational Optimization and Applications
Authors: ,
Keywords: programming: integer
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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