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.
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Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms, and Applications. Birkhäuser, Boston (1999)
Herman, G.T., Kuba, A. (eds.): Advances in Discrete Tomography and Its Applications. Birkhäuser, Basel (to appear, 2006)
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)
Herman, G.T., Kuba, A.: Discrete tomography in medical imaging. Proc. of the IEEE 91, 1612–1626 (2003)
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)
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)
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)
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)
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)
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)
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Weber, S., Nagy, A., Schüle, T., Schnörr, C., Kuba, A. (2006). A Benchmark Evaluation of Large-Scale Optimization Approaches to Binary Tomography. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds) Discrete Geometry for Computer Imagery. DGCI 2006. Lecture Notes in Computer Science, vol 4245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11907350_13
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DOI: https://doi.org/10.1007/11907350_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47651-1
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