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Reduced inverse Born series: a computational study
Summary
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.
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.
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