Abstract
We present a new method of computerized tomography based on linear programming. The approach is based on three main ideas: covering the set of pixels by digital lines, introducing a variable of maximal error in the linear constraints and adding in the objective function an entropy term.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging. IEEE Computer Society Press, Los Alamitos (1988)
Herman, G., Lent, A.: Iterative reconstruction algorithms. Comput. Biol. Med. 6, 273–274 (1976)
Gordon, R., Herman, G.: Reconstruction of pictures from their projections. Communication of the ACM 14, 759–768 (1971)
Gordon, R.: A tutorial on ART (Algebraic Reconstruction Techniques). IEEE Transactions on Nuclear Science NS-21, 31–43 (1974)
Ben-Tal, A., Margalit, T., Nemirovski, A.: The ordered subsets mirror descent optimization method with applications to tomography. SIAM J. Optimization 12, 79–108 (2001)
Aharoni, R., Herman, G., Kuba, A.: Binary vectors partially determined by linear equation systems. Discrete Mathematics 171, 1–16 (1997)
Kuba, A., Herman, G.: Discrete Tomography: Foundations, Algorithms and Applications. Birkhaüser, Basel (1999)
Fishburn, P., Schwander, P., Shepp, L., Vanderbei, R.: The discrete radon transform and its approximate inversion via linear programming. Discrete Applied Math. 75, 39–61 (1997)
Gritzmann, P., de Vries, S., Wiegelmann, M.: Approximating binary images from discrete X-rays. SIAM J. Optimization 11, 522–546 (2000)
Weber, S., Schnörr, C., Hornegger, J.: A linear programming relaxation for binary tomography with smoothness priors. In: Int. Workshop on Combinatorial Image Analysis IWCIA 2003. Electronic Notes in Discrete Math., vol. 12, Elsevier, Amsterdam (2003)
Brunetti, S., Daurat, A.: Stability in discrete tomography: Linear programming, additivity and convexity. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 398–408. Springer, Heidelberg (2003)
Hajdu, L., Tijdeman, R.: An algorithm for discrete tomography. Linear Algebra and Appl. 339, 147–169 (2001)
Reveillès, J.P.: Géométrie discrète, calcul en nombres entiers et algorithmique. In: Thèse d’état, Université ULP - Strasbourg (1991)
Weber, S., Schüle, T., Hornegger, C.S., Discrete, J.: tomography by convex-concave regularization and d.c. programming. Technical report, Mannheim University (2003)
Schrijver, A.: Theory of Linear and Integer Programming. J. Wiley and Sons, Chichester (1986)
Wunderling, R.: Paralleler und Objektorientierter Simplex-Algorithmus. PhD thesis, ZIB TR 96-09, Berlin (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Feschet, F., Gérard, Y. (2005). Computerized Tomography with Digital Lines and Linear Programming. In: Andres, E., Damiand, G., Lienhardt, P. (eds) Discrete Geometry for Computer Imagery. DGCI 2005. Lecture Notes in Computer Science, vol 3429. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31965-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-31965-8_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25513-0
Online ISBN: 978-3-540-31965-8
eBook Packages: Computer ScienceComputer Science (R0)