Abstract
Over the last two decades, there has been a considerable amount of work on the inverse scattering problems, especially for quantum and acoustic waves1–10. But up to now, it is still very difficult to reconstruct a higher dimensional scatterer from the observed scattered field outside the scatterer. The difficulties in reconstructing a higher dimensional scatterer lie in diffraction effects. What is the way out? One notes that the one dimensional inverse scattering problems have been worked out well1–5. The key ideas in solving the one dimensional inverse scattering problems are as follows:
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(1)
Introduce a field transform to simplify the relation between the underlying scatterer (or potential) and the direct scattered field.
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(2)
Use the completeness relation for this direct scattering solution system.
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© 1993 Springer Science+Business Media New York
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Lu, ZQ. (1993). Exact Reconstruction of a Scatterer and Completeness Relations for the Scattering Solutions. In: Wei, Y., Gu, B. (eds) Acoustical Imaging. Acoustical Imaging, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2958-3_18
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DOI: https://doi.org/10.1007/978-1-4615-2958-3_18
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