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.

中文翻译：

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声电断层扫描中的声速不确定性

声电断层扫描 (AET) 的目标是通过传播超声波穿透物体时在物体边界上测量的外部静电电流和电压重建物体中未知电导率的图像。这个问题是一个耦合物理逆问题。通常假设并需要传播超声波的准确知识，但实际上，由于对物体内部声波速度的了解不准确，因此很难或可能不可能跟踪传播波。在这项工作中，我们对波速的不确定性进行建模，并为功率密度和电导率制定了合适的重建方法。我们还建立了理论误差界限，并表明建议的方法可以理解为逆问题的正则化方案。最后，我们从数值乳房组织模型中模拟波速，并通过计算探索重建中错误的严重程度。我们的结果表明，在合理的声速不确定性下，可靠的重建是可能的。