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Related Experiment Videos

Inverse scattering solutions by a sinc basis, multiple source, moment method--Part I: Theory.

S A Johnson, M L Tracy

    Ultrasonic Imaging
    |October 1, 1983
    PubMed
    Summary

    This study introduces a novel method for solving inverse scattering problems without approximations. The new approach, utilizing multiple sources and overdetermined data, offers stable and unique solutions for wave equations, even with complex field interactions.

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    Area of Science:

    • Computational physics
    • Electromagnetics
    • Wave propagation

    Background:

    • Inverse scattering problems are often ill-posed, especially with single monochromatic sources.
    • Existing methods frequently rely on perturbation approximations, limiting their applicability.
    • Handling wave phenomena with attenuation and refraction poses significant challenges.

    Purpose of the Study:

    • To present a novel, non-perturbative method for solving the inverse scattering problem for the Helmholtz wave equation.
    • To address challenges posed by inhomogeneous media, attenuation, and refraction.
    • To establish a well-posed, stable, and unique solution framework for inverse scattering.

    Main Methods:

    • Application of the method of moments with sinc basis and delta testing functions for problem discretization.

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  • Utilizing multiple sources and overdetermined data collection.
  • Constraining fields and complex refractive index to be spatially band-limited.

    • Main Results:

    • The developed method is applicable to cases with weak to moderate attenuation and moderate to strong refraction.
    • Computer simulations indicate the new problem formulation is well-posed.
    • The method yields unique and stable solutions, even with noisy data.

    Conclusions:

    • The novel method provides a robust solution for the inverse scattering problem without approximations.
    • The approach effectively handles complex wave interactions, including attenuation and refraction.
    • This work advances the field by offering a stable and unique solution for challenging inverse scattering scenarios.