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Second-order iterative approach to inverse scattering: numerical results
1Dipartimento di Ingegneria dell'Informazione, Seconda Universita di Napoli, Aversa, Italy. pierri@unina.it
Summary
A new iterative algorithm reconstructs dielectric profiles using quadratic inversion, offering improved accuracy over linear methods. This approach enhances dielectric profile function reconstruction from scattered field data.
Area of Science:
- Electromagnetics and Optics
- Computational Physics
- Inverse Problems
Background:
- Accurate reconstruction of dielectric profiles is crucial for understanding material properties and electromagnetic wave interactions.
- Existing linear iterative inversion algorithms face convergence limitations for certain profile functions.
Purpose of the Study:
- To introduce and validate a novel iterative algorithm for dielectric profile reconstruction.
- To compare the performance of the proposed quadratic inversion algorithm against traditional linear methods.
Main Methods:
- Development of an iterative algorithm solving quadratic inversion problems at each step.
- Second-order approximation of the scattering operator using a reference profile function.
- Numerical simulations in scalar two-dimensional geometry using far-zone scattered field data.
Main Results:
- The proposed quadratic iterative algorithm demonstrates convergence to the actual solution.
- Linear iterative inversion algorithms show convergence limitations for specific profile function classes.
- The quadratic model reconstructs a broader class of functions compared to the linear model.
Conclusions:
- The quadratic iterative algorithm provides a more robust and accurate method for dielectric profile reconstruction.
- The enhanced approximation in the quadratic model is beneficial for profiles with larger norms.
- The study confirms the theoretical advantages of the quadratic approach through numerical examples.