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

Abstract

To determine the mechanical properties and morphology of solid materials, tomographic imaging at relatively low frequencies is a promising option. However, mode conversions between compressional and shear waves require the use of non-linear tomographic methods taking multiple scattering into account. For this reason, we presented an approach based on the Kaczmarz method. A necessary condition of convergence is that the accumulated phase difference between a wave propagating through the background medium and the correct solution has to be smaller than π. It means that the higher the contrasts, the lower the imaging frequency has to be chosen. In this work, we demonstrate that this restrictive convergence condition is mainly due to calculating the adjoint operator for the real wave field. By applying an analytical extension of the excitation and calculating the adjoint operator for the complex wave fields the imaging of the materials with high contrasts can be performed in higher frequencies.