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Solution of the nonlinear inverse scattering problem by T-matrix completion. II. Simulations
Howard W Levinson1, Vadim A Markel2
1Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Physical Review. E
|November 15, 2016
Summary
Data-compatible T-matrix completion (DCTMC) effectively solves nonlinear inverse problems using scalar wave simulations. This method reconstructs object shapes and quantitative contrast, vital for imaging applications like ultrasound tomography.
Area of Science:
- Computational physics
- Applied mathematics
- Wave propagation
Background:
- Nonlinear inverse problems present significant challenges in scientific imaging.
- Existing methods often struggle with large datasets and strong nonlinearities.
- Part I of this series established the theoretical framework for DCTMC.
Purpose of the Study:
- To present simulation results for the data-compatible T-matrix completion (DCTMC) method.
- To demonstrate DCTMC's applicability to inverse scattering of scalar waves.
- To validate DCTMC for strongly nonlinear inverse problems with extensive data.
Main Methods:
- Utilized the scalar wave equation as the underlying mathematical model.
- Employed DCTMC for reconstructing medium susceptibility.
- Performed simulations relevant to ultrasound and seismic tomography.
Main Results:
- DCTMC proved to be a viable method for complex inverse problems.
- The method successfully reconstructed object shapes.
- Quantitative contrast, indicative of variable sound speed, was accurately determined.
Conclusions:
- DCTMC is a robust technique for solving strongly nonlinear inverse problems.
- The method offers accurate shape and contrast reconstruction for tomographic imaging.
- DCTMC is suitable for large-scale inverse scattering problems.
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