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    Area of Science:

    • Applied Mathematics
    • Signal Processing
    • Computational Physics

    Background:

    • Inverse scattering problems are crucial in various scientific fields.
    • Exploiting scatterer sparsity in wavelet bases is a key technique.
    • Existing methods may lead to over-smoothed solutions at discontinuities.

    Purpose of the Study:

    • To propose an iteratively reweighted L1 norm regularization scheme for inverse scattering.
    • To leverage the sparsity of wavelet coefficients more effectively.
    • To improve solution accuracy and avoid over-smoothing at discontinuities.

    Main Methods:

    • Utilizing an iteratively reweighted L1 norm minimization scheme.
    • Integrating L1 and L2 norm minimization for balanced regularization.
    • Applying the method within each iteration of the Born Iterative Method (BIM).

    Main Results:

    • The proposed method effectively utilizes sparsity in detail wavelet coefficients.
    • Reconstructions are independent of the initial weight choices.
    • Demonstrated effectiveness in 2D inverse scattering examples.

    Conclusions:

    • The iteratively reweighted L1 norm method enhances inverse scattering solutions.
    • This approach provides improved accuracy and better handling of discontinuities.
    • The method offers a robust alternative to existing techniques.