Consistency Conditions for Discrete Tomography

• Autorzy: Hajdu L. , Tijdeman R.

Identyfikatory

DOI

10.3233/FI-2017-1593

• Języki publikacji: EN

Abstrakty

EN

For continuous tomography Helgason and Ludwig developed consistency conditions. They were used by others to overcome defects in the measurements. In this paper we introduce a consistency criterion for discrete tomography. We indicate how the consistency criterion can be used to overcome defects in measurements.

Słowa kluczowe

EN

discrete tomography; linear dependencies; global dependencies

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2017
• Tom: Vol. 155, nr 4
• Strony: 425--447
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Hajdu L.

• Institute of Mathematics, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary

autor

Tijdeman R.

• Mathematical Institute, Leiden University, 2300 RA Leiden, P.O. Box 9512, The Netherlands

Bibliografia

• [1] Batenburg KJ, FortesW, Hajdu L, Tijdeman R. Bounds on the difference between reconstructions in binary tomography, LNCS 6607, Springer 2011, pp. 369–380. doi:10.1007/978-3-642-19867-0_31.
• [2] Brunetti S, Dulio P, Peri C. Characterization of {1; 0; 1} valued functions in discrete tomography under sets of four directions, In: Discrete Geometry for Computer Imaginery, LNCS 6607, Springer 2011, pp. 394–405. doi: 10.1007/978-3-642-19867-0_33.
• [3] Brunetti S, Dulio P, Peri C. Discrete tomography determination of bounded lattice sets from four X-rays, Discr. Appl. Math. 2013;161(15):2281–2292. URL https://doi.org/10.1016/j.dam.2012.09.010.
• [4] Brunetti S, Dulio P, Peri C. Discrete tomography determination of bounded sets in Zn, Discr. Appl. Math. 2015;183:20–30. URL https://doi.org/10.1016/j.dam.2014.01.016.
• [5] van Dalen BE. Dependencies between line sums, Master’s thesis, Univ. Leiden, 2007. URL https://www.math.leidenuniv.nl/scripties/DalenMaster.pdf.
• [6] van Dalen BE. Discrete tomography, Ph.D. Thesis, Univ. Leiden, 2011.
• [7] van Dalen BE, Hajdu L, Tijdeman R. Bounds for discrete tomography solutions, Indag. Math. 2013;24(2):391–402. URL https://doi.org/10.1016/j.indag.2012.12.005.
• [8] Hajdu L. Unique reconstruction of bounded sets in discrete tomography, Electronic Notes in Discrete Mathematics, 2005;20:15–25. URL https://doi.org/10.1016/j.endm.2005.04.002.
• [9] Hajdu L, Tijdeman R. Algebraic aspects of discrete tomography, J. Reine Angew. Math., 2001;534:119–128. URL https://doi.org/10.1515/crll.2001.037.
• [10] Hajdu L, Tijdeman R. Algebraic aspects of emission tomography with absorption, Theor. Comput. Sci., 2003;290(3):2169–2181. URL https://doi.org/10.1016/S0304-3975(02)00585-6.
• [11] Hajdu L, Tijdeman R. Algebraic discrete tomography, in: Advances in Discrete Tomography and its Applications, G.T. Herman, A. Kuba, eds., Birkhäuser, 2007, pp. 55–81. doi:10.1007/978-0-8176-4543-4_4.
• [12] Hajdu L, Tijdeman R. Bounds for approximate discrete tomography solutions, SIAM J. Discrete Math. 2013;27(2):1055–1066. doi:10.1137/120883268.
• [13] Helgason S. The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 1965;113:153–180. doi:10.1007/BF02391776.
• [14] Ludwig D. The Radon transform on Euclidean space, Comm. Pure Appl. Math. 1966;19:49–81. doi:10.1002/cpa.3160190105.
• [15] Natterer F. The mathematics of computerized tomography, SIAM, Philadelphia, 2001. URL http://dx.doi.org/10.1137/1.9780898719284.
• [16] Stolk AP. Discrete tomography for integer-valued functions, PhD-thesis, Leiden University, 2011.
• [17] Stolk AP, Batenburg KJ. An algebraic framework for discrete tomography SIAM J. Discrete Math., 2010;24(3):1056–1079. doi:10.1137/090766693.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).