Mueller J L, Siltanen S
Department of Mathematics and School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80525.
Department of Mathematics and Statistics, University of Helsinki, Finland.
Inverse Probl. 2020 Sep;36(9). doi: 10.1088/1361-6420/aba2f5. Epub 2020 Aug 31.
Electrical impedance tomography (EIT) is an imaging modality where a patient or object is probed using harmless electric currents. The currents are fed through electrodes placed on the surface of the target, and the data consists of voltages measured at the electrodes resulting from a linearly independent set of current injection patterns. EIT aims to recover the internal distribution of electrical conductivity inside the target. The inverse problem underlying the EIT image formation task is nonlinear and severely ill-posed, and hence sensitive to modeling errors and measurement noise. Therefore, the inversion process needs to be regularized. However, traditional variational regularization methods, based on optimization, often suffer from local minima because of nonlinearity. This is what makes regularized direct (non-iterative) methods attractive for EIT. The most developed direct EIT algorithm is the D-bar method, based on Complex Geometric Optics solutions and a nonlinear Fourier transform. Variants and recent developments of D-bar methods are reviewed, and their practical numerical implementation is explained.
电阻抗断层成像（EIT）是一种成像方式，通过使用无害电流对患者或物体进行探测。电流通过放置在目标表面的电极输入，数据由在电极处测量到的电压组成，这些电压是由一组线性独立的电流注入模式产生的。EIT旨在恢复目标内部电导率的分布。EIT图像形成任务所基于的逆问题是非线性且严重不适定的，因此对建模误差和测量噪声很敏感。所以，反演过程需要进行正则化。然而，基于优化的传统变分正则化方法由于非线性常常会陷入局部极小值。这就是正则化直接（非迭代）方法对EIT具有吸引力的原因。最成熟的直接EIT算法是基于复几何光学解和非线性傅里叶变换的D-bar方法。本文回顾了D-bar方法的变体和最新进展，并解释了它们的实际数值实现。
