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An approach to inverse scattering problems

M Saito, T Hayashi

    Bioelectromagnetics
    |January 1, 1982
    PubMed
    Summary
    This summary is machine-generated.

    Investigating the inverse scattering problem using ultrasonic fields allows for object structure determination. Scattered wave data on a surrounding circle is sufficient for image reconstruction via successive approximations.

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    Area of Science:

    • Medical image processing
    • Applied physics
    • Wave propagation

    Background:

    • The inverse scattering problem is crucial for reconstructing object details from wave interactions.
    • Ultrasonic imaging is a key medical diagnostic tool, necessitating efficient inverse scattering methods.

    Purpose of the Study:

    • To investigate the inverse scattering problem for weakly inhomogeneous 2D objects using ultrasonic fields.
    • To demonstrate that scattered wave data from a surrounding circle is sufficient for object reconstruction.

    Main Methods:

    • Derivation of the fundamental equation for scattered waves in integral and differential forms.
    • Formulation of object structure information into a single term dependent on wavenumber and angles.
    • Application of successive approximation techniques for image reconstruction.

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    Main Results:

    • The study shows that scattered waves observed on a circle are sufficient to specify the object's structure.
    • A method is proposed to summarize this information in a single function.
    • Computational examples for a cylindrical object illustrate the approximation methods.

    Conclusions:

    • The inverse scattering problem in medical imaging, particularly with ultrasonic fields, can be solved using scattered wave data.
    • Successive approximation offers a viable approach for image reconstruction when analytical solutions are unavailable.