Variable density linear acoustic inverse problem

Area of Science:

• Acoustic inverse problems
• Diffraction tomography
• Wave scattering

Background:

• Solving the linear acoustic inverse problem for material properties like density and compressibility is challenging.
• Traditional methods may struggle with simultaneous reconstruction of both parameters.

Purpose of the Study:

• To develop a method for simultaneously reconstructing object density (rho) and compressibility (kappa).
• To utilize frequency diversity and diffraction tomography principles for improved inverse problem solutions.

Main Methods:

• Employed diffraction tomography (DT) principles with plane wave incidence and far-field receivers.
• Utilized frequency diversity to obtain independent measurements.
• Applied the Born approximation to relate pressure fields to spatial Fourier transforms of density and compressibility.
• Solved a least squares problem using multi-frequency data.
• Developed a regularization method to address inaccuracies from low spatial frequencies.

Main Results:

• Successfully reconstructed both density and compressibility simultaneously.
• Identified inaccuracies caused by low spatial frequencies in object spectra.
• Demonstrated significant improvement in reconstruction quality after applying regularization.
• Achieved good reconstructions for low-contrast objects.

Conclusions:

• Frequency diversity is key for simultaneous density and compressibility reconstruction in acoustic inverse problems.
• Regularization is essential to mitigate inaccuracies and achieve reliable results.
• The developed method shows promise for accurate material property imaging.