Journal of Mathematical Imaging and Vision ( IF 2 ) Pub Date : 2021-01-11 , DOI: 10.1007/s10851-020-01006-y Changyou Li , Mirza Karamehmedović , Ekaterina Sherina , Kim Knudsen
The inverse problem in acousto-electric tomography concerns the reconstruction of the electric conductivity in a body from knowledge of the power density function in the interior of the body. This interior power density results from currents prescribed at boundary electrodes, and it can be obtained through electro-static boundary measurements together with auxiliary acoustic probing. Previous works on acousto-electric tomography used the continuum model for the electrostatic boundary conditions; however, from Electrical Impedance Tomography, it is known that the complete electrode model is much more realistic and accurate. In this paper, the inverse problem of acousto-electric tomography is posed using the (smoothened) complete electrode model, and a reconstruction method based on the Levenberg–Marquardt iteration is formulated in appropriate function spaces. This results in a system of partial differential equations to be solved in each step. To increase the computational efficiency and stability, a strategy based on both the complete electrode model and the continuum model is proposed. The method is implemented numerically for a two-dimensional scenario, and the algorithm is tested on two different numerical phantoms, a heart and lung model and a human brain model. Several numerical experiments are carried out confirming the feasibility, accuracy and stability of the developed method.
中文翻译:
基于完整电极模型的Levenberg-Marquardt声电层析成像算法
声电层析成像中的反问题涉及根据人体内部的功率密度函数的知识来重建人体的电导率。内部功率密度是由边界电极处规定的电流产生的,可以通过静电边界测量以及辅助声学探测获得。以前的声电层析成像研究使用了连续边界模型来确定静电边界条件。然而,从电阻抗层析成像技术可以看出,完整的电极模型更加真实和准确。在本文中,使用(平滑的)完整电极模型提出了声电层析成像的反问题,在适当的函数空间中提出了基于Levenberg-Marquardt迭代的重构方法。这导致在每个步骤中都要求解偏微分方程组。为了提高计算效率和稳定性,提出了一种基于完整电极模型和连续模型的策略。该方法在二维情况下以数字方式实现,并且对该算法在两个不同的数字体模(心肺模型和人脑模型)上进行了测试。进行了几次数值实验,证实了该方法的可行性,准确性和稳定性。提出了一种基于完整电极模型和连续模型的策略。该方法在二维情况下以数字方式实现,并且对该算法在两个不同的数字体模(心肺模型和人脑模型)上进行了测试。进行了几次数值实验,证实了该方法的可行性,准确性和稳定性。提出了一种基于完整电极模型和连续模型的策略。该方法在二维情况下以数字方式实现,并且对该算法在两个不同的数字体模(心肺模型和人脑模型)上进行了测试。进行了几次数值实验,证实了该方法的可行性,准确性和稳定性。