Regularization methods for inverse problems in X-ray tomography

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 7804, Issue , 2010, Pages

  Titarenko, Valeriy ^a   Bradley, Robert ^a   Martin, Christopher ^a   Withers, Philip J ^a   Titarenko, Sofya ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

a priori information; regularization; ring artefacts

Indexed keywords

ILL POSED PROBLEM; PRIORI INFORMATION; REGULARIZATION; REGULARIZATION METHODS; RING ARTEFACTS; SMOOTH FUNCTIONS; SPATIAL VARIABLES; SUPPRESSION ALGORITHM; TIKHONOV FUNCTIONAL; X-RAY TOMOGRAPHY;

CAMERAS; CCD CAMERAS; IMAGING SYSTEMS; SCINTILLATION COUNTERS; TOMOGRAPHY; X RAYS;

INVERSE PROBLEMS;

EID: 78649429366     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.860260     Document Type: Conference Paper

References (25)

1. Hadamard, J., "Sur les problèmes aux dérivées partielles et leur signification physique," Princeton University Bulletin 13, 49-52 (1902).
2. Tikhonov, A. N., "Solution of incorrectly formulated problems and the regularization method," Sov. Math., Dokl. 5, 1035-1038 (1963).
3. Tikhonov, A. N., "Regularization of incorrectly posed problems," Sov. Math., Dokl. 4, 1624-1627 (1963).
4. Tikhonov, A. N. and Arsenin, V. Y., [Solutions of ill-posed problems], John Wiley & Sons, New York (1977).
5. Tikhonov, A. N., Goncharsky, A. V., Stepanov, V. V., and Yagola, A. G., [Numerical methods for the solution of ill-posed problems], Kluwer Academic Publishers, Dordrecht (1995).
6. Engl, H. W., Hanke, M., and Neubauer, A., [Regularization of inverse problems], Kluwer Academic Publishers, Dordrecht (1996).
7. Yagola, A. G., Leonov, A. S., and Titarenko, V. N., "Data errors and an error estimation for ill-posed problems," Inverse Problems in Science and Engineering 10(2), 117-129 (2002).
8. Natterer, F. and Wübbeling, F., [Mathematical methods in image reconstruction], SIAM, Philadelphia, PA (2007).
9. Feldkamp, L. A., Davis, L. C., and Kress, J. W., "Practical cone-beam algorithm," Journal of the Optical Society of America A 1(6), 612-619 (1984).
10. Kirillov, A. A., "A problem of I.M. Gel'fand," Sov. Math., Dokl. 2, 268-269 (1961).
11. Tuy, H. K., "An inversion formula for cone-beam reconstruction, " SIAM Journal on Applied Mathematics 43(3), 546-552 (1983).
12. Stock, S. R., [Microcomputed tomography: methodology and applications], CRC Press, Boca Raton, FL (2008).
13. Boin, M. and Haibel, A., "Compensation of ring artefacts in synchrotron tomographic images," Optics Express 14(25), 12071-12075 (2006). (Pubitemid 44907547)
14. Raven, C., "Numerical removal of ring artifacts in microtomography," Rev. Sci. Instrum. 69, 2978-2980 (August 1998). (Pubitemid 128494796)
15. Walls, J. R., Sled, J. G., Sharpe, J., and Henkelman, R. M., "Correction of artefacts in optical projection tomography," Phys. Med. Biol. 50, 4645-4665 (October 2005). (Pubitemid 41361523)
16. Sijbers, J. and Postnov, A., "Reduction of ring artefacts in high resolution micro-CT reconstructions," Phys. Med. Biol. 49(14), N247-N253 (2004). (Pubitemid 39140019)
17. Davis, G. R. and Elliott, J. C., "X-ray microtomography scanner using time-delay integration for elimination of ring artefacts in the reconstructed image," Nucl. Instr. Meth. A 394, 157-162 (July 1997).
18. Banhart, J., [Advanced tomographic methods in matherial research and engineering], Oxford University Press, Oxford (2008).
19. Mahajan, V. N., [Optical imaging and aberrations: Part II. Wave diffraction optics], SPIE Press, Bellingham, WA (2001).
20. Titarenko, S., Titarenko, V., Kyrieleis, A., and Withers, P. J., "A ring artifact suppression algorithm based on a priori information," Appl. Phys. Lett. 95, 071113 (August 2009).
21. Titarenko, S., Withers, P. J., and Yagola, A., "An analytical formula for ring artefact suppression in X-ray tomography," Appl. Math. Lett. (2010). submitted.
22. Titarenko, S., Titarenko, V., Kyrieleis, A., and Withers, P. J., "A priori information in a regularized sinogram-based method for removing ring artefacts in tomography," J. Synchrotron Radiation 17(4), 540-549 (2010).
23. Titarenko, S. S. and Yagola, A. G., "Ring artefact suppression in real-time x-ray tomography," Moscow University Physics Bulletin 65(1), 65-67 (2010).
24. Hsu, H. P., [Schaum's outline of signals and systems], Schaum's Outlines (1995).
25. Titarenko, S., Titarenko, V., Kyrieleis, A., Withers, P. J., and De Carlo, F., "Suppression of ring artefacts when tomographing anisotropically attenuating samples," J. Synchrotron Radiation (2010). submitted.