Imaging ultrasonic dispersive guided wave energy in long bones using linear radon transform

Area of Science:

• Ultrasonic wave propagation and analysis
• Signal processing for material characterization
• Biomedical engineering and non-destructive testing

Background:

• Multichannel analysis of dispersive ultrasonic energy requires accurate mapping from the time-distance (t-x) domain to frequency-wavenumber (f-k) or frequency-phase velocity (f-c) domains.
• The conventional 2-D Fourier transform (FT) method for this mapping suffers from limited resolution, hindering the discrimination of wave modes.
• The resolving power of the FT is heavily dependent on the aperture of the recorded data.

Purpose of the Study:

• To present and evaluate a linear Radon transform (RT) as an alternative method for imaging dispersive ultrasonic energies.
• To enhance the focusing power and resolution in the transformed plane for better wave mode discrimination.
• To compare the robustness and performance of different RT formulations against the traditional FT.

Main Methods:

• Implementation of a linear Radon transform (RT) posed as an inverse problem, incorporating regularization strategies for enhanced focusing.
• Utilized Cauchy regularization for the high-resolution RT.
• Compared three RT forms (adjoint, damped least-squares, high-resolution) with the 2-D Fourier transform (FT) using simulated and cervine bone data.

Main Results:

• The Radon transform (RT) offers improved resolution in the dispersion panel, up to approximately 300% greater than the Fourier transform (FT).
• The high-resolution RT demonstrated superior imaging resolution (at least 110% improvement) compared to other RT forms and the FT.
• The RT method is less sensitive to data aperture limitations than the FT and can handle unevenly spaced records.

Conclusions:

• The linear Radon transform, particularly the high-resolution variant, is a valuable tool for imaging dispersive guided wave energies.
• This method significantly enhances imaging resolution, enabling better discrimination of wave modes, especially under limited aperture conditions.
• The RT provides a more robust and higher-resolution alternative to the FT for analyzing complex ultrasonic wave fields.