Nonlinear reconstruction of bulk and shear moduli variations using the kazmarcz method

Abstract

Nonlinear ultrasound diffraction tomography reconstructs material parameters of a medium from transmitted and scattered sound waves taking into account multiple scattering. A few nonlinear approaches propose algorithms to reconstruct the spatially varying speed of sound (SoS) or alternatively the spatially varying compressibility and mass density. These methods consider longitudinal wave propagation, but not the shear wave propagation which is important in elastic media like in muscle tissue or bone. Here, we present an extension of a nonlinear reconstruction algorithm based on the Kaczmarz method to reconstruct bulk and shear moduli in isotropic solids simultaneously. The morphology of the solid inclusion can be imaged using this approach. This is a first step towards the reconstruction of hard tissues like bone and cartilage possibly enabling the assessment of the cortical thickness of bones.

Increasing the robustness and convergence rate of the Kaczmarz method in reconstructing the speed of sound in solid materials using analytic signals

“…In our previous work [11], we presented a new version of our algorithm to reconstruct the full elastodynamic wave parameters for an isotropic solid in presence of shear waves considering a constant density. However, for high contrasts between the object and background material the stability of the algorithm was an issue.…”