Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2017, Article ID 4850317, 8 pages
https://doi.org/10.1155/2017/4850317
Research Article

Relaxation Factor Optimization for Common Iterative Algorithms in Optical Computed Tomography

1School of Electrical Engineering and Electronic Information, Xihua University, Chengdu 610039, China
2Sichuan Province Key Laboratory of Signal and Information Processing, Xihua University, Chengdu 610039, China
3Hiroshima Institute of Technology, Hiroshima 731-5193, Japan

Correspondence should be addressed to Wenbo Jiang; moc.liamg@gnaijobnewsac

Received 12 April 2017; Revised 6 June 2017; Accepted 12 June 2017; Published 16 July 2017

Academic Editor: Eric Feulvarch

Copyright © 2017 Wenbo Jiang and Xiaohua Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Gilbert, “Iterative methods for the three-dimensional reconstruction of an object from projections,” Journal of Theoretical Biology, vol. 36, no. 1, pp. 105–117, 1972. View at Publisher · View at Google Scholar · View at Scopus
  2. R. L. Kashyap and M. C. Mittal, “Picture reconstruction from projections,” IEEE Transactions on Computers, vol. C-24, no. 9, pp. 915–923, 1975. View at Publisher · View at Google Scholar · View at Scopus
  3. G. T. Herman and W. N. Brouw, Image Reconstruction from Projections, Academic Press, 1980. View at MathSciNet
  4. K. M. Hanson and G. W. Wecksung, “Local basis-function approach to computed tomography,” Applied Optics, vol. 24, no. 23, pp. 4028–4039, 1985. View at Publisher · View at Google Scholar · View at Scopus
  5. K. T. Smith and F. Keinert, “Mathematical foundations of computed tomography,” Applied Optics, vol. 24, no. 23, pp. 3950–3957, 1985. View at Publisher · View at Google Scholar · View at Scopus
  6. H. Szu, “Computed tomography for optical computing,” Optical and Hybrid Computing, vol. 634, pp. 475–479, 1986. View at Google Scholar
  7. F. Keinert, “Inversion of K-plane transforms and applications in computer tomography,” SIAM Review, vol. 31, no. 2, pp. 273–298, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  8. P. M. V. Subbarao, P. Munshi, and K. Muralidhar, “Performance evaluation of iterative tomographic algorithms applied to reconstruction of a three-dimensional temperature field,” Numerical Heat Transfer, Part B, vol. 31, no. 3, pp. 347–372, 1997. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Mishra, K. Muralidhar, and P. Munshi, “Robust MART algorithm for tomographic applications,” Numerical Heat Transfer, Part B, vol. 35, no. 4, pp. 485–506, 1999. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Mishra, K. Muralidhar, and P. Munshi, “Experimental study of rayleigh-Benard convection at intermediate Rayleigh numbers using interferometric tomography,” Fluid Dynamics Research, vol. 25, no. 5, pp. 231–255, 1999. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Mishra, K. Muralidhar, and P. Munshi, “Interferometric study of Rayleigh-Benard convection using tomography with limited projection data,” Experimental Heat Transfer, vol. 12, no. 2, pp. 117–136, 1999. View at Publisher · View at Google Scholar · View at Scopus
  12. D. Verhoeven, “Limited-data computed tomography algorithms for the physical sciences,” Applied Optics, vol. 32, no. 20, pp. 3736–3754, 1993. View at Publisher · View at Google Scholar · View at Scopus
  13. D. W. Watt, “Column-relaxed algebraic reconstruction algorithm for tomography with noisy data,” Applied Optics, vol. 33, no. 20, pp. 4420–4427, 1994. View at Publisher · View at Google Scholar · View at Scopus
  14. X. Wan, Y. Gao, Q. Wang, S. Le, and S. Yu, “Limited-angle optical computed tomography algorithms,” Optical Engineering, vol. 42, no. 9, pp. 2659–2669, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. G. T. Herman and A. Lent, “Iterative reconstruction algorithms,” Computers in Biology and Medicine, vol. 6, no. 4, pp. 273–294, 1976. View at Publisher · View at Google Scholar · View at Scopus
  16. I. Voo, E. C. Mavrofrides, and C. A. Puliafito, “Clinical applications of optical coherence tomography for the diagnosis and management of macular diseases,” Ophthalmology Clinics of North America, vol. 17, no. 1, pp. 21–31, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. W. Drexler and J. G. Fujimoto, “Optical coherence tomography in ophthalmology,” Journal of Biomedical Optics, vol. 12, no. 4, article 041201, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. A. K. Suomalainen, A. Salo, S. Robinson, and J. S. Peltola, “The 3DX multi image micro-CT device in clinical dental practice,” Dentomaxillofacial Radiology, vol. 36, no. 2, pp. 80–85, 2007. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Youn, K. C. Min, and H. K. Kim, “Clinical micro-CT for dental imaging,” in Proceedings of SPIE, vol. 7258, pp. 31–41, 2009.
  20. F. Long, M. Ozturk, M. Wolff, X. Intes, and S. Kotha, “Dental imaging using mesoscopic fluorescence molecular tomography: an ex vivo feasibility study,” Photonics, vol. 1, no. 4, pp. 488–502, 2014. View at Publisher · View at Google Scholar
  21. R. R. Alfano, “Optical tomography breast imaging,” in Proceedings of SPIE, pp. 2979–197, 1997.
  22. Y. Ardeshirpour and Q. Zhu, “Optical tomography method that accounts for tilted chest wall in breast imaging,” Journal of Biomedical Optics, vol. 15, no. 4, article 041515, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. M. L. Flexman, M. A. Khalil, R. A. Abdi et al., “Digital optical tomography system for dynamic breast imaging,” Journal of Biomedical Optics, vol. 16, no. 7, article 076014, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. J. A. Izatt, M. D. Kulkarni, S. Yazdanfar, J. K. Barton, and A. J. Welch, “In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography,” Optics Letters, vol. 22, no. 18, pp. 1439–1441, 1997. View at Publisher · View at Google Scholar · View at Scopus
  25. M. Wellner, O. Bernus, S. F. Mironov, and A. M. Pertsov, “Multiplicative optical tomography of cardiac electrical activity,” Physics in Medicine and Biology, vol. 51, no. 18, pp. 4429–4446, 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. G. Isenberg and M. V. Sivak Jr., “Gastrointestinal optical coherence tomography,” Techniques in Gastrointestinal Endoscopy, vol. 5, no. 2, pp. 94–101, 2003. View at Publisher · View at Google Scholar · View at Scopus
  27. W. Kang, X. Qi, H. Wang, and A. M. Rollins, Optical Coherence Tomography for Gastrointestinal Endoscopy, Springer International Publishing, 2015.
  28. R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography,” Journal of Theoretical Biology, vol. 29, no. 3, pp. 471–481, 1970. View at Publisher · View at Google Scholar · View at Scopus
  29. A. D. Verhoeven, “Multiplicative algebraic computed tomographic algorithms for the reconstruction of multidirectional interferometric data,” Optical Engineering, vol. 32, no. 2, pp. 410–419, 1993. View at Publisher · View at Google Scholar
  30. A. H. Andersen and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm,” Ultrasonic Imaging, vol. 6, no. 1, pp. 81–94, 1984. View at Publisher · View at Google Scholar · View at Scopus
  31. F. Natterer, The Mathematics of Computerized Tomography, John Wiley & Sons, 1986. View at MathSciNet
  32. H. Stark, J. W. Woods, I. Paul, and R. Hingorani, “Direct Fourier reconstruction in computer tomography,” IEEE Transactions on Acoustics Speech & Signal Processing, vol. 9, no. 2, pp. 237–245, 1981. View at Google Scholar
  33. M. Tabei and M. Ueda, “Backprojection by upsampled fourier series expansion and interpolated FFT,” IEEE Transactions on Image Processing, vol. 1, no. 1, pp. 77–87, 1992. View at Publisher · View at Google Scholar · View at Scopus
  34. C. M. Vest and I. Prikryl, “Tomography by iterative convolution: empirical study and application to interferometry,” Applied Optics, vol. 23, no. 14, pp. 2433–2440, 1984. View at Publisher · View at Google Scholar · View at Scopus
  35. Y. Gao, W. Jiang, Q. Yu, and X. Tang, “Research on improved reconstruction algorithms of optical tomography based on incomplete data,” Optik, vol. 120, no. 18, pp. 951–958, 2009. View at Publisher · View at Google Scholar · View at Scopus