Czasopismo
2013
|
Vol. 125, nr 3/4
|
239--259
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
Discrete tomography deals with tomographic reconstruction of greyscale images for which the set of possible grey levels is discrete and small. Here, we develop a discrete approximate reconstruction algorithm. Our algorithm computes an image that has only grey values belonging to a given finite set. It also guarantees that the difference between the given projections and the projections of the reconstructed discrete image is bounded. The bound, which is computable, is independent of the image size. We present reconstruction experiments for a range of phantom images and a varying number of grey values.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
239--259
Opis fizyczny
Bibliogr. 21 poz., rys., wykr.
Twórcy
autor
- Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, The Netherlands, joost.batenburg@cwi.nl
autor
- Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, The Netherlands, wagner.fortes@cwi.nl
autor
- Mathematical Institute, Leiden University, The Netherlands, tijdeman@math.leidenuniv.nl
Bibliografia
- [1] Batenburg, K. J.: A network flow algorithm for reconstructing binary images from continuous X-rays, J. Math. Im. Vision, 30(3), 2008, 231-248.
- [2] Batenburg, K. J., Sijbers, J.: DART: a Practical Reconstruction Algorithm for Discrete Tomography, IEEE Trans. Image Processing, 20(9), 2011, 2542-2553.
- [3] Ben-Israel, A., Greville, T. N. E.: Generalized inverses: Theory and Applications, Canadian Math. Soc., 2002.
- [4] Beck, J., Fiala, T.: Integer-making theorems, Discr. Appl. Math., (3), 1981, 1-8.
- [5] Bjorck, A.: Numerical Methods for Least Square Problems, SIAM, Linkoping University, Sweden, 1996.
- [6] Censor, Y.: Row-action methods for huge and sparse systems and their applications, SIAM review, 23(4), 1981,444-466.
- [7] Gardner, R. J., Gritzmann, P., Prangenberg, D.: On the computational complexity of reconstructing lattice sets from their X-rays, Discrete Math., 202, 1999,45-71.
- [8] Gordon, R., Bender, R., Herman, G. T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography, J. Theor. Biol., 29(3), 1970,471-481.
- [9] Hajdu, L., Tijdeman, R.: Bounds for approximate discrete tomography solutions, arXiv, 1207.3933, 2012.
- [10] Herman, G. T.: Fundamentals of Computerized Tomography: Image reconstruction from projections, Springer, 2009.
- [11] Herman, G. T., Kuba, A., Eds.: Discrete Tomography: Foundations, Algorithms and Applications, Birkhauser, Boston, 1999.
- [12] Herman, G. T., Kuba, A., Eds.: Advances in Discrete Tomography and its Applications, Birkhauser, Boston, 2007.
- [13] Jinschek, J. R., Batenburg, K. J., Calderon, H. A., Kilaas, R., Radmilovic, V., Kisielowski, C.: 3-D reconstruction of the atomic positions in a simulated gold nanocrystal based on discrete tomography, Ultramicroscopy, 108(6), 2007, 589-604.
- [14] Joseph, P. M.: An improved algorithm for reprojecting rays through pixel images, IEEE Trans. Med. Imag., MI-1(3), 1982, 192-196.
- [15] Kak, A. C., Slaney, M.: Principles of Computerized Tomographic Imaging, SIAM, 2001.
- [16] Natterer, F.: The mathematics of computerized tomography, John Wiley & Sons, 1986, ISBN 0471909599, 9780471909590.
- [17] Saad, Y.: Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, PA, USA, 2003, ISBN 0898715342.
- [18] Schule, T., Schnorr, C., Weber, S., Homegger, J.: Discrete tomography by convex-concave regularization and D.C. programming, Discr. Appl. Math, 151, 2005, 229-243.
- [19] Van Aert, S., Batenburg, K. J., Rossell, M., Erni, R., Van Tendeloo, G.: Three-dimensional atomic imaging of crystalline nanoparticles, Nature, 470, 2011, 374-377.
- [20] van der Sluis, A., van der Vorst, H. A.: SIRT and CG-type methods for the iterative solution of sparse linear least-squares problems, Linear Algebra Appl., 130, 1990, 257-302.
- [21] Zhua, J., Li, X., Ye, Y., Wang, G.: Analysis on the strip-based projection model for discrete tomography, Discrete Appl. Math., 156(12), 2008, 2359-2367.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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