High-Resolution Imaging of Dispersive Ultrasonic Guided Waves in Human Long Bones Using Regularized Radon Transforms

Abstract

Ultrasound is an indispensable imaging modality to monitor soft tissues in diagnostic radiology. Research into ultrasound has resulted in technology developments and extension of its use beyond soft tissue imaging. The use of ultrasound to probe hard tissues is not yet a common practice but in recent years modest interest has been generated to use quantitative ultrasound in bone evaluation. This is due to several advantages of ultrasound over ionizing techniques: lack of ionizing radiation, sensitivity to the mechanical elasticity of bone tissues, portability, and low cost. Recent studies using axial-transmission technique have shown that ultrasonic guided waves, which propagate within cortical bone, have great potential to characterize mechanical and structural properties of the cortical waveguide. Multi-channel dispersion analysis of ultrasonic guided waves requires a reliable mean to map the data from the time-distance domain to the frequency-phase velocity domain. In this work, linear Radon transform using various regularization strategies is considered to enhance the transform focusing power to image dispersive guide-wave energies. Four forms of linear Radon solution: adjoint, damped least-squares, Cauchy-regularized, and l₁-regularized Radon transform were applied to the simulated and in-vivo experimental data and the results were compared. Among the regularization strategies, the l₁-regularization renders a highly-sparse solution and images dispersion energies with the best focusing resolution. The high-resolution dispersion maps allow better wave-mode discrimination and separation. The results of this study suggest the l₁-regularized Radon transform as a valuable tool to image dispersive ultrasonic guided-wave energies propagating in long bones.