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

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

http://dx.doi.org/10.1364/JOSAA.15.001545

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### Abstract

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

**History**

Original Manuscript: July 30, 1997

Revised Manuscript: December 22, 1997

Manuscript Accepted: January 12, 1998

Published: June 1, 1998

**Citation**

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)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-6-1545

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### References

- L. Nicolaides, A. Mandelis, “Image-enhanced thermal-wave slice diffraction tomography with numerically simulated reconstructions,” Inverse Probl. 13, 1339–1412 (1997).
- 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]
- O. Pade, A. Mandelis, “Computational thermal-wave slice tomography with backpropagation and transmission reconstructions,” Rev. Sci. Instrum. 64, 3548–3562 (1993). [CrossRef]
- A. Mandelis, “Theory of photothermal-wave diffraction and interference in condensed media,” J. Opt. Soc. Am. A 6, 298–308 (1989). [CrossRef]
- A. Mandelis, “Green’s functions in thermal-wave physics: Cartesian coordinate representations,” J. Appl. Phys. 78, 647–655 (1995). [CrossRef]
- 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]
- 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]
- 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]
- O. Pade, A. Mandelis, “Thermal-wave slice tomography using wave-field reconstruction,” Inverse Probl. 10, 185–197 (1994). [CrossRef]
- 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]
- 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).
- T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997). [CrossRef]
- 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]
- G. Beylkin, R. Coifman, V. Rokhlin, “Fast wavelet transforms and numerical algorithms. I,” Commun. Pure Appl. Math. 44, 141–183 (1991). [CrossRef]
- 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.
- 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]
- 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]
- Y. Meyer, Wavelets and Operators (Cambridge U. Press, Cambridge, 1995).
- R. F. Harrington, Field Computations by Moment Methods (Macmillan, New York, 1968).
- 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]
- M. V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software (A. K. Peters, Wellesley, Mass., 1994).
- 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]
- I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–996 (1988). [CrossRef]
- G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, Mass., 1996).
- 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]
- P. E. Gill, W. Murry, M. H. Wright, Practical Optimization (Academic, San Diego, 1981).
- A. Gersztenkorn, J. B. Bednar, L. R. Lines, “Robust iterative inversion for the one-dimensional acoustic wave equation,” Geophysics 51, 357–368 (1986). [CrossRef]
- 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]
- 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).
- 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]
- 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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