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

Authors:
Geir Dahl;Truls Flatberg
Affiliations:
Centre of Mathematics for Application and Department of Informatics, University of Oslo, Oslo, Norway 0316;Centre of Mathematics for Application and Department of Informatics, University of Oslo, Oslo, Norway 0316
Venue:
Computational Optimization and Applications
Year:
2009

Citing 7
Cited 0

Integer and combinatorial optimization

Integer and combinatorial optimization
Layering strategies for creating exploitable structure in linear and integer programs

Mathematical Programming: Series A and B
Boundary Detection by Constrained Optimization

IEEE Transactions on Pattern Analysis and Machine Intelligence
Bundle-based relaxation methods for multicommodity capacitated fixed charge network design

Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Approximating Binary Images from Discrete X-Rays

SIAM Journal on Optimization
Optimization and reconstruction of hv-convex (0, 1)-matrices

Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Nonlinear Optimization

Nonlinear Optimization

Quantified Score

Hi-index	0.00

Visualization

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.