Algebraic aspects of emission tomography with absorption. (English) Zbl 1044.68152
Summary: In a previous paper the authors analysed the classical discrete tomography problem to construct a \(0-1\)-matrix with given line sums in some given directions. One of the physical representations is that material at the lattice points corresponding to 1’s emit units of radiation and that the radiation is measured along the given lines. In the present paper they extend their approach to the case that the intermediate material is absorbing the radiation. They generalise results obtained by A. Kuba and M. Nivat [Linear Algebra Appl. 339, No. 1–3, 171–194 (2001; Zbl 1004.65056)].
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 68U10 | Computing methodologies for image processing |
| 92C55 | Biomedical imaging and signal processing |
Citations:
Zbl 1004.65056References:
| [1] | Hajdu, L.; Tijdeman, R., Algebraic aspects of discrete tomography, J. Reine Angew. Math., 534, 119-128 (2001) · Zbl 1058.92029 |
| [2] | G.T. Herman, A. Kuba (Eds.), Discrete Tomography: Foundations, Algorithms and Applications, Birkhäuser, Boston, 1999.; G.T. Herman, A. Kuba (Eds.), Discrete Tomography: Foundations, Algorithms and Applications, Birkhäuser, Boston, 1999. · Zbl 0946.00014 |
| [3] | A. Kuba, M. Nivat, Reconstruction of discrete sets from projections in case of absorption, Tech. Reports, Institute of Informatics, University of Szeged, 2000.; A. Kuba, M. Nivat, Reconstruction of discrete sets from projections in case of absorption, Tech. Reports, Institute of Informatics, University of Szeged, 2000. · Zbl 1043.68807 |
| [4] | A. Kuba, M. Nivat, Reconstruction of discrete sets with absorption, Discrete Geometry in Computer Imaginery, Lecture Notes in Computer Science, vol. 1953, Springer, Berlin, 2000, pp. 137-148.; A. Kuba, M. Nivat, Reconstruction of discrete sets with absorption, Discrete Geometry in Computer Imaginery, Lecture Notes in Computer Science, vol. 1953, Springer, Berlin, 2000, pp. 137-148. · Zbl 1043.68807 |
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