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Mathematical Problems in Engineering
Volume 2012, Article ID 478295, 27 pages
http://dx.doi.org/10.1155/2012/478295
Research Article

Multidimensional Wave Field Signal Theory: Transfer Function Relationships

Department of Mechanical Engineering, University of Ottawa, Ottawa, ON, Canada K1N 6N5

Received 29 August 2011; Accepted 20 September 2011

Academic Editor: Carlo Cattani

Copyright © 2012 Natalie Baddour. 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. A. Mandelis, “Theory of photothermal-wave diffraction and interference in condensed media,” Journal of the Optical Society of America A, vol. 6, no. 2, pp. 298–308, 1989. View at Publisher · View at Google Scholar
  2. A. Mandelis, Diffusion-Wave Fields. Mathematical methods and Green Function, Springer-Verlag, New York, NY, USA, 2001. View at Zentralblatt MATH
  3. M. Slaney and A. C. Kak, Principles of Computerized Tomographic Imaging, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1988. View at Zentralblatt MATH
  4. M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Review of Scientific Instruments, vol. 77, no. 4, pp. 041101.1–041101.22, 2006. View at Publisher · View at Google Scholar
  5. A. Mandelis and C. Feng, “Frequency-domain theory of laser infrared photothermal radiometric detection of thermal waves generated by diffuse-photon-density wave fields in turbid media,” Physical Review E—Statistical Nonlinear, and Soft Matter Physics, vol. 65, no. 2, pp. 021909/1–021909/19, 2002. View at Google Scholar
  6. A. Mandelis, Y. Fan, G. Spirou, and A. Vitkin, “Development of a photothermoacoustic frequency swept system: theory and experiment,” Journal De Physique. IV : JP, vol. 125, pp. 643–647, 2005. View at Publisher · View at Google Scholar
  7. A. Mandelis, R. J. Jeon, S. Telenkov, Y. Fan, and A. Matvienko, “Trends in biothermophotonics and bioacoustophotonics of tissues,” in Proceedings of the International Society for Optics and Photonics (SPIE '05), vol. 5953, pp. 1–15, The International Society for Optical Engineering, Warsaw, Poland, 2005.
  8. C. L. Matson, “A diffraction tomographic model of the forward problem using diffuse photon density waves,” Optics Express, vol. 1, no. 1, pp. 6–11, 1997. View at Google Scholar
  9. L. Nicolaides and A. Mandelis, “Image-enhanced thermal-wave slice diffraction tomography with numerically simulated reconstructions,” Inverse Problems, vol. 13, no. 5, pp. 1393–1412, 1997. View at Publisher · View at Google Scholar
  10. L. Nicolaides, M. Munidasa, and A. Mandelis, “Thermal-wave infrared radiometric slice diffraction tomography with back-scattering and transmission reconstructions: experimental,” Inverse Problems, vol. 13, no. 5, pp. 1413–1425, 1997. View at Google Scholar
  11. O. Pade and A. Mandelis, “Computational thermal-wave slice tomography with backpropagation and transmission reconstructions,” Review of Scientific Instruments, vol. 64, no. 12, pp. 3548–3562, 1993. View at Publisher · View at Google Scholar
  12. O. Pade and A. Mandelis, “Thermal-wave slice tomography using wave field reconstruction,” in Proceedings of the 8th International Topical Meeting on Photoacoustic and Photothermal Phenomena, vol. 4, 1994.
  13. S. A. Telenkov, G. Vargas, J. S. Nelson, and T. E. Milner, “Coherent thermal wave imaging of subsurface chromophores in biological materials,” Physics in Medicine and Biology, vol. 47, no. 4, pp. 657–671, 2002. View at Publisher · View at Google Scholar
  14. S. A. Telenkov, J. S. Nelson, and T. E. Milner, “Tomographic reconstruction of tissue chromophores using thermal wave imaging,” Laser Tissue Interaction XIII, vol. 4617, pp. 40–46, 2002. View at Publisher · View at Google Scholar
  15. S. A. Telenkov and A. Mandelis, “Fourier-domain biophotoacoustic subsurface depth selective amplitude and phase imaging of turbid phantoms and biological tissue,” Journal of Biomedical Optics, vol. 11, no. 4, 2006. View at Publisher · View at Google Scholar
  16. N. Baddour, “Theory and analysis of frequency-domain photoacoustic tomography,” Journal of the Acoustical Society of America, vol. 123, no. 5, pp. 2577–2590, 2008. View at Publisher · View at Google Scholar
  17. N. Baddour, “A multidimensional transfer function approach to photo-acoustic signal analysis,” Journal of the Franklin Institute, vol. 345, no. 7, pp. 792–818, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. N. Baddour, “Fourier diffraction theorem for diffusion-based thermal tomography,” Journal of Physics A, vol. 39, no. 46, pp. 14379–14395, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. A. Mandelis, “Theory of photothermal wave diffraction tomography via spatial Laplace spectral decomposition,” Journal of Physics A, vol. 24, no. 11, pp. 2485–2505, 1991. View at Publisher · View at Google Scholar
  20. A. Mandelis, “Green's functions in thermal-wave physics: cartesian coordinate representations,” Journal of Applied Physics, vol. 78, no. 2, pp. 647–655, 1995. View at Publisher · View at Google Scholar
  21. M. Puschel and J. M. F. Moura, “Algebraic signal processing theory: cooley-Tukey type algorithms for DCTs and DSTs,” IEEE Transactions on Signal Processing, vol. 56, no. 4, pp. 1502–1521, 2008. View at Publisher · View at Google Scholar
  22. M. Puschel, “Algebraic signal processing theory: An overview,” in Proceedings of the IEEE 12th Digital Signal Processing Workshop and 4th IEEE Signal Processing Education Workshop, pp. 386–391, Moose, Wyo, USA, 2006. View at Publisher · View at Google Scholar
  23. M. Puschel and J. Moura, “Algebraic signal processing theory: foundation and 1-D time,” IEEE Transactions on Signal Processing, vol. 56, no. 8, pp. 3572–3585, 2008. View at Publisher · View at Google Scholar
  24. M. Puschel and J. M. F. Moura, “Algebraic signal processing theory: 1-D space,” IEEE Transactions on Signal Processing, vol. 56, no. 8, pp. 3586–3599, 2008. View at Publisher · View at Google Scholar
  25. M. Puschel and J. M. F. Moura, “The algebraic structure in signal processing: time and space,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '06), vol. 5, 2006. View at Publisher · View at Google Scholar
  26. M. Puschel and M. Rotteler, “Algebraic signal processing theory: 2-D spatial hexagonal lattice,” IEEE Transactions on Image Processing, vol. 16, no. 6, pp. 1506–1521, 2007. View at Publisher · View at Google Scholar
  27. M. Puschel and M. Rotteler, “Algebraic signal processing theory: cooley-Tukey type algorithms on the 2-D hexagonal spatial lattice,” Applicable Algebra in Engineering, Communication and Computing, vol. 19, no. 3, pp. 259–292, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. N. Baddour, “Operational and convolution properties of two-dimensional Fourier transforms in polar coordinates,” Journal of the Optical Society of America A, vol. 26, no. 8, pp. 1767–1778, 2009. View at Publisher · View at Google Scholar
  29. N. Baddour, “Operational and convolution properties of three-dimensional Fourier transforms in spherical polar coordinates,” Journal of the Optical Society of America, vol. 27, no. 10, pp. 2144–2155, 2010. View at Google Scholar
  30. N. Baddour, “Theory and analysis of frequency-domain photoacoustic tomography,” Journal of the Acoustical Society of America, vol. 123, no. 5, pp. 2577–2590, 2008. View at Google Scholar
  31. G. S. Chirikjian and A. B. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis, CRC Press, Boca Raton, Fla, USA, 2000.
  32. G. S. Chirikjian and A. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups, Academic Press, New York, NY, USA, 2001.
  33. R. Piessens, “The Hankel transform,” in The Transforms and Applications Handbook, vol. 2, pp. 9.1–9.30, CRC Press, Boca Raton, Fla, USA, 2000. View at Google Scholar
  34. “Spherical harmonics—wikipedia, the free encyclopedia,” http://en.wikipedia.org/wiki/Spherical_harmonics, Accessed: 16-Nov-2009.
  35. J. R. Driscoll and D. M. Healy, “Computing Fourier transforms and convolutions on the 2-sphere,” Advances in Applied Mathematics, vol. 15, no. 2, pp. 202–250, 1994. View at Publisher · View at Google Scholar
  36. N. Baddour, “Multidimensional wave field signal theory: mathematical foundations,” AIP Advances, vol. 1, no. 2, p. 022120, 2011. View at Publisher · View at Google Scholar
  37. M. Abramowitz and I. Stegun, Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York, NY, USA, 1964.