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    This study introduces a reduced inverse Born series for scalar wave inverse scattering problems. This simplified series shows improved performance compared to standard methods in numerical simulations.

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    Area of Science:

    • Physics
    • Applied Mathematics

    Background:

    • The inverse scattering problem aims to determine the properties of an object from scattered wave data.
    • The inverse Born series is a common method for solving inverse scattering problems, but can be computationally intensive.

    Purpose of the Study:

    • To develop a more efficient method for solving the inverse scattering problem for scalar waves.
    • To introduce and analyze a reduced inverse Born series.

    Main Methods:

    • Investigating conditions for pairwise cancellation of terms in the inverse Born series.
    • Deriving a reduced inverse Born series.
    • Comparing the reduced series with the full inverse Born series and the Newton-Kantorovich method using numerical simulations.

    Main Results:

    • Identified conditions under which terms in the inverse Born series cancel in pairs.
    • Developed a reduced inverse Born series with fewer terms at each order.
    • Numerical simulations demonstrated the effectiveness of the reduced series.

    Conclusions:

    • The reduced inverse Born series offers a potentially more efficient approach to solving scalar wave inverse scattering problems.
    • The findings provide a foundation for further development and application of this method.