Sound speed uncertainty in Acousto-Electric Tomography

The goal in acousto-electric tomography (AET) is to reconstruct an image of the unknown electric conductivity in an object from exterior electrostatic currents and voltages that are measured on the boundary of the object while the object is penetrated by propagating ultrasound waves. This problem is a coupled-physics inverse problem. Accurate knowledge of the propagating ultrasound wave is usually assumed and required, but in practice tracking the propagating wave is very hard, or potentially impossible, due inexact knowledge of the object's interior acoustic wave speed. In this work, we model uncertainty in the wave speed, and formulate a suitable reconstruction method for the power density and conductivity. We also establish theoretical error bounds, and show that the suggested approach can be understood as a regularization scheme for the inverse problem. Finally, we simulate the wave speed from a numerical breast tissue model, and computationally explore the severity of the error in the reconstructions. Our results show that with reasonable sound speed uncertainty, reliable reconstruction is possible.