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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 6 — Jun. 1, 1998
  • pp: 1545–1556

Nonlinear inverse scattering methods for thermal-wave slice tomography: a wavelet domain approach

Eric L. Miller, Lena Nicolaides, and Andreas Mandelis  »View Author Affiliations

JOSA A, Vol. 15, Issue 6, pp. 1545-1556 (1998)

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A wavelet domain, nonlinear inverse scattering approach is presented for imaging subsurface defects in a material sample, given observations of scattered thermal waves. Unlike methods using the Born linearization, our inversion scheme is based on the full wave-field model describing the propagation of thermal waves. Multiresolution techniques are employed to regularize and to lower the computational burden of this ill-posed imaging problem. We use newly developed wavelet-based regularization methods to resolve better the edge structures of defects relative to reconstructions obtained with smoothness-type regularizers. A nonlinear approximation to the exact forward-scattering model is introduced to simplify the inversion with little loss in accuracy. We demonstrate this approach on cross-section imaging problems by using synthetically generated scattering data from transmission and backprojection geometries.

© 1998 Optical Society of America

OCIS Codes
(100.7410) Image processing : Wavelets
(170.6960) Medical optics and biotechnology : Tomography
(290.0290) Scattering : Scattering

Original Manuscript: July 30, 1997
Revised Manuscript: December 22, 1997
Manuscript Accepted: January 12, 1998
Published: June 1, 1998

Eric L. Miller, Lena Nicolaides, and Andreas Mandelis, "Nonlinear inverse scattering methods for thermal-wave slice tomography: a wavelet domain approach," J. Opt. Soc. Am. A 15, 1545-1556 (1998)

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  1. L. Nicolaides, A. Mandelis, “Image-enhanced thermal-wave slice diffraction tomography with numerically simulated reconstructions,” Inverse Probl. 13, 1339–1412 (1997).
  2. L. Nicolaides, M. Munidasa, A. Mandelis, “Image-enhanced thermal-wave slice diffraction tomography with backpropagation and transmission reconstructions: experimental,” Inverse Probl. 13, 1413–1425 (1997). [CrossRef]
  3. O. Pade, A. Mandelis, “Computational thermal-wave slice tomography with backpropagation and transmission reconstructions,” Rev. Sci. Instrum. 64, 3548–3562 (1993). [CrossRef]
  4. A. Mandelis, “Theory of photothermal-wave diffraction and interference in condensed media,” J. Opt. Soc. Am. A 6, 298–308 (1989). [CrossRef]
  5. A. Mandelis, “Green’s functions in thermal-wave physics: Cartesian coordinate representations,” J. Appl. Phys. 78, 647–655 (1995). [CrossRef]
  6. C. Torres-Verdı́n, T. M. Habashy, “Rapid 2.5-D forward modeling and inversion via a new nonlinear scattering approximation,” Radio Sci. 29, 1051–1079 (1994). [CrossRef]
  7. T. M. Habashy, W. C. Chew, E. Y. Chow, “Simultaneous reconstruction of permittivity and conductivity profiles in a radially inhomogeneous slab,” Radio Sci. 21, 635–645 (1986). [CrossRef]
  8. T. Wang, M. Oristaglio, A. Tripp, G. Hohmann, “Inversion of diffusive transient electromagnetic data by a conjugate-gradient method,” Radio Sci. 29, 1143–1156 (1994). [CrossRef]
  9. O. Pade, A. Mandelis, “Thermal-wave slice tomography using wave-field reconstruction,” Inverse Probl. 10, 185–197 (1994). [CrossRef]
  10. T. M. Habashy, R. W. Groom, B. R. Spies, “Beyond the Born and Rytov approximations: a nonlinear approach to electromagnetic scattering,” J. Geophys. Res. 98, 1759–1775 (1993). [CrossRef]
  11. D. Lesselier, B. Duchene, “Wave-field inversion of objects in stratified environments: from backpropagation schemes to full solutions,” in Review of Radio Science, W. R. Stone, ed. (Oxford U. Press, Oxford, UK, 1996).
  12. T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997). [CrossRef]
  13. E. L. Miller, A. S. Willsky, “Wavelet-based methods for the nonlinear inverse scattering problem using the extended Born approximation,” Radio Sci. 31, 51–67 (1996). [CrossRef]
  14. G. Beylkin, R. Coifman, V. Rokhlin, “Fast wavelet transforms and numerical algorithms. I,” Commun. Pure Appl. Math. 44, 141–183 (1991). [CrossRef]
  15. M. Bertero, “Linear inverse and Ill-posed problems,” in Advances in Electronics and Electron Physics, P. Hawkes, ed. (Academic, Boston, 1989), Vol. 75, pp. 1–120.
  16. E. L. Miller, A. S. Willsky, “Multiscale, statistically-based inversion scheme for the linearized inverse scattering problem,” IEEE Trans. Geosci. Remote Sens. 34, 346–357 (1996). [CrossRef]
  17. M. Bertero, C. D. Mol, E. R. Pike, “Linear inverse problems with discrete data. II. Stability and regularisation,” Inverse Probl. 4, 573–594 (1988). [CrossRef]
  18. Y. Meyer, Wavelets and Operators (Cambridge U. Press, Cambridge, 1995).
  19. R. F. Harrington, Field Computations by Moment Methods (Macmillan, New York, 1968).
  20. B. Wang, J. C. Moulder, J. P. Basart, “Wavelets in the solution of the volume integral equation: application to eddy current modeling,” J. Appl. Phys. 81, 6397–6406 (1997). [CrossRef]
  21. M. V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software (A. K. Peters, Wellesley, Mass., 1994).
  22. A. Cohen, I. Daubechies, B. Jawerth, P. Vial, “Multiresolution analysis, wavelets and fast algorithms on an interval,” Appl. Comput. Harmon. Anal. 1, 54–81 (1993). [CrossRef]
  23. I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–996 (1988). [CrossRef]
  24. G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, Mass., 1996).
  25. M. Bertero, C. D. Mol, E. R. Pike, “Linear inverse problems with discrete data. I: General formulation and singular system analysis,” Inverse Probl. 1, 301–330 (1985). [CrossRef]
  26. P. E. Gill, W. Murry, M. H. Wright, Practical Optimization (Academic, San Diego, 1981).
  27. A. Gersztenkorn, J. B. Bednar, L. R. Lines, “Robust iterative inversion for the one-dimensional acoustic wave equation,” Geophysics 51, 357–368 (1986). [CrossRef]
  28. P. Charbonnier, L. Blanc-Feraud, G. Aubert, M. Barlund, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311 (1997). [CrossRef] [PubMed]
  29. E. L. Miller, “The application of multiscale and statistical techniques to the solution of inverse problems,” (MIT Laboratory for Information and Decision Systems, Cambridge, Mass., 1994).
  30. B. Alpert, G. Beylkin, R. Coifman, V. Rokhlin, “Wavelets for the fast solution of second-kind integral equations,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 14, 159–184 (1993). [CrossRef]
  31. E. L. Miller, A. S. Willsky, “Multiscale, statistical anomaly detection analysis and algorithms for linearized inverse scattering problems,” Multidimens. Syst. Signal Process. 8, 151–184 (1997). [CrossRef]

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