Advertisement

A Benchmark Evaluation of Large-Scale Optimization Approaches to Binary Tomography

  • Stefan Weber
  • Antal Nagy
  • Thomas Schüle
  • Christoph Schnörr
  • Attila Kuba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)

Abstract

Discrete tomography concerns the reconstruction of functions with a finite number of values from few projections. For a number of important real-world problems, this tomography problem involves thousands of variables. Applicability and performance of discrete tomography therefore largely depend on the criteria used for reconstruction and the optimization algorithm applied. From this viewpoint, we evaluate two major optimization strategies, simulated annealing and convex-concave regularization, for the case of binary-valued functions using various data sets. Extensive numerical experiments show that despite being quite different from the viewpoint of optimization, both strategies show similar reconstruction performance as well as robustness to noise.

References

  1. 1.
    Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms, and Applications. Birkhäuser, Boston (1999)zbMATHGoogle Scholar
  2. 2.
    Herman, G.T., Kuba, A. (eds.): Advances in Discrete Tomography and Its Applications. Birkhäuser, Basel (to appear, 2006)Google Scholar
  3. 3.
    Krimmel, S., Baumann, J., Kiss, Z., Kuba, A., Nagy, A., Stephan, J.: Discrete tomography for reconstruction from limited view angles in non-destructive testing. Electronic Notes in Discrete Mathematics 20, 455–474 (2005)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Herman, G.T., Kuba, A.: Discrete tomography in medical imaging. Proc. of the IEEE 91, 1612–1626 (2003)CrossRefGoogle Scholar
  5. 5.
    Liao, H.Y., Herman, G.T.: A method for reconstructing label images from a few projections, as motivated by electron microscopy. Annals of Operations Research (to appear)Google Scholar
  6. 6.
    Weber, S., Schüle, T., Schnörr, C., Hornegger, J.: A linear programming approach to limited angle 3d reconstruction from dsa projections. Special Issue of Methods of Information in Medicine 4, 320–326 (2004)Google Scholar
  7. 7.
    Schüle, T., Schnörr, C., Weber, S., Hornegger, J.: Discrete tomography by convex-concave regularization and D.C. programming. Discrete Applied Mathematics 151, 229–243 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Schnörr, C., Schüle, T., Weber, S.: Variational Reconstruction with DC-Programming. In: Herman, G.T., Kuba, A. (eds.) Advances in Discrete Tomography and Its Applications. Birkhäuser, Boston (to appear, 2006)Google Scholar
  9. 9.
    Birgin, E.G., Martínez, J.M., Raydan, M.: Algorithm 813: SPG - software for convex-constrained optimization. ACM Transactions on Mathematical Software 27, 340–349 (2001)zbMATHCrossRefGoogle Scholar
  10. 10.
    Metropolis, N.A., Rosenbluth, A.T., Rosenbluth, M., Teller, E.: Equation of state calculation by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Stefan Weber
    • 1
  • Antal Nagy
    • 2
  • Thomas Schüle
    • 1
  • Christoph Schnörr
    • 1
  • Attila Kuba
    • 2
  1. 1.Dept. Math. & Comp. Science, CVGPR-GroupUniversity of MannheimMannheimGermany
  2. 2.Department of Image Processing and Computer GraphicsUniversity of SzegedSzegedHungary

Personalised recommendations