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Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

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Fast inverse scattering solutions using the distorted Born iterative method and the multilevel fast multipole

Andrew J Hesford¹, Weng C Chew

¹Department of Electrical and Computer Engineering, University of Rochester, Rochester, New York 14627, USA. hesford@ece.rochester.edu

The Journal of the Acoustical Society of America

|August 17, 2010

Summary

This summary is machine-generated.

The distorted Born iterative method (DBIM) accelerates inverse scattering solutions by integrating the multilevel fast multipole algorithm (MLFMA) for faster forward computations. This approach enhances imaging efficiency for complex material property variations.

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Area of Science:

Computational electromagnetics
Inverse scattering theory
Numerical methods for wave phenomena

Background:

Nonlinear inverse scattering problems require iterative solutions, often computationally intensive.
The distorted Born iterative method (DBIM) approximates solutions through successive linearizations.
High computational burden arises from repeated forward solutions in DBIM.

Purpose of the Study:

To reduce the computational cost of the DBIM for inverse scattering problems.
To improve the efficiency of imaging large or high-contrast variations in medium properties.
To demonstrate the effectiveness of integrating advanced algorithms for solving complex wave phenomena.

Main Methods:

Implemented the multilevel fast multipole algorithm (MLFMA) as a forward solver within the DBIM framework.
Utilized Kaczmarz-like iterations with partial measurements to accelerate convergence.
Applied DBIM with MLFMA to inverse scattering problems involving volumetric scatterers.

Main Results:

Achieved linear time complexity for forward solutions using MLFMA for volumetric scatterers.
Demonstrated significant reduction in computational demands by leveraging data redundancy in scattering elements.
Successfully applied the inverse method to imaging problems up to ten wavelengths in dimension.
Validated the efficiency of the MLFMA forward solver and the overall inverse imaging technique.

Conclusions:

The integration of MLFMA as a forward solver substantially alleviates the computational burden of DBIM.
The combined approach enables efficient and accurate imaging of complex subsurface structures.
This method offers a promising advancement for solving challenging nonlinear inverse scattering problems.