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Least Squares Reconstruction of Binary Images using Eigenvalue Optimization

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Compstat

Abstract

The goal of this paper is to present an application to binary image least-squares estimation of some recent results in the semi-definite programming approximation theory of some combinatorial problems due to Goemans and Williamson, Yu. Nesterov and others. In particular, we show in a very simple fashion that a good suboptimal solution may be obtained via eigenvalue optimization.

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References

  1. Goemans M. and Williamson D., Improved approximation algorithms for maximum cut and satisfiability problems using semi-definite programming. Journal of the ACM (1996).

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  2. Hiriart-Urruty J.-B. and Lemaréchal C., Convex analysis and optimization algorithms, Springer (1993).

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  3. Nesterov Yu., Quality of semi-definite relaxation for nonconvex quadratic optimization, Core discussion paper 9719 Center for Operations Research & Econometrics, Louvain-la-Neuve (1997)

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  4. Oustry F., A second order bundle method to minimize the maximum eigen-value function, Math. Programming, 89 no. 1 Ser. A, pp. 1–30 (2000).

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  5. Chrétien S. and Corset F., Eigenvalue relaxation of some binary linear least-squares estimation problems, Technical Report, Mathematics department, Université de Franche-Comté, in preparation.

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Author information

Authors and Affiliations

  1. Département de mathématiques, Université de Franche-Comté, 16 route de Gray, 25030, Besançon Cedex, France

    Stéphane Chrétien

  2. INRIA Rhône-Alpes, 655 avenue de l’Europe, Montbonnot, 38334, Saint Ismier Cedex, France

    Franck Corset

Authors
  1. Stéphane Chrétien
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  2. Franck Corset
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Editor information

Editors and Affiliations

  1. CASE — Centre of Applied Statistics and Economics, Humboldt-Universität zu Berlin, Spandauer Straße 1, 10178, Berlin, Germany

    Wolfgang Härdle

  2. Wirtschaftswissenschaftliche Fakultät, Institut für Statistik und Ökonometrie, Humboldt-Universität zu Berlin, Spandauer Straße 1, 10178, Berlin, Germany

    Bernd Rönz

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© 2002 Springer-Verlag Berlin Heidelberg

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Chrétien, S., Corset, F. (2002). Least Squares Reconstruction of Binary Images using Eigenvalue Optimization. In: Härdle, W., Rönz, B. (eds) Compstat. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57489-4_63

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  • DOI: https://doi.org/10.1007/978-3-642-57489-4_63

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1517-7

  • Online ISBN: 978-3-642-57489-4

  • eBook Packages: Springer Book Archive

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