Nonlinear reconstruction of compressibility and density variations using the Kaczmarz method

Nonlinear ultrasound diffraction tomography reconstructs material parameters of a medium from transmitted and scattered sound waves taking into account multiple scattering, which is important in the presence of strongly scattering media like in breast tissue or the abdominal wall. Most nonlinear approaches propose algorithms to reconstruct the spatially varying speed of sound (SoS), which is equivalent to a spatially varying compressibility under the assumption of constant mass density. Here, we present an extension of a nonlinear reconstruction algorithm based on the Kaczmarz method to reconstruct both, density and compressibility simultaneously. We investigate errors arising from neglecting realistic density changes and demonstrate the improvements that can be introduced in the estimation of speed of sound by applying the proposed method.