IEEE Trans Med Imaging. 2019 Nov;38(11):2533-2544. doi: 10.1109/TMI.2019.2905245. Epub 2019 Mar 18.
This paper presents a B-spline-based shape reconstruction approach for electrical impedance tomography (EIT). In the proposed approach, the conductivity distribution to be reconstructed is assumed to be piecewise constant. The geometry of the inclusions is parameterized using B-spline curves, and the EIT forward solver is modified as a set of control points representing the inclusions' boundary to the data on the domain boundary. The low-order representation decreases the computational demand and reduces the ill-posedness of the EIT reconstruction problem. The performance of the proposed B-spline-based approach is tested with simulations that demonstrate the most popular biomedical application of EIT: lung imaging. The approach is experimentally validated using water tank data. In addition, robustness studies of the proposed approach considering varying initial guesses, inaccurately known contact impedances, differing numbers of control points, and degree of B-spline are performed. The simulation and experimental results show that the B-spline-based approach offers improvements in image quality in comparison to the traditional Fourier series-based reconstruction approach, as measured by quantitative metrics such as relative size coverage ratio and relative contrast. Inasmuch, the proposed approach is demonstrated to offer clear improvement in the ability to preserve the sharp properties of the inclusions to be imaged.
本文提出了一种基于 B 样条的电阻抗断层成像（EIT）形状重建方法。在提出的方法中，假设待重建的电导率分布是分段常数的。用 B 样条曲线对包含物的几何形状进行参数化，并将 EIT 正问题求解器修改为一组代表包含物边界的控制点，以表示边界域上的数据。低阶表示降低了计算需求，并降低了 EIT 重建问题的不适定性。通过模拟测试了基于 B 样条的方法的性能，这些模拟演示了 EIT 最流行的生物医学应用：肺部成像。该方法使用水箱数据进行了实验验证。此外，还考虑了不同的初始猜测、不准确的已知接触阻抗、不同数量的控制点和 B 样条的程度进行了稳健性研究。模拟和实验结果表明，与传统的基于傅里叶级数的重建方法相比，基于 B 样条的方法在图像质量方面有所提高，这可以通过相对大小覆盖率和相对对比度等定量指标来衡量。此外，还证明了该方法在保留要成像的包含物的尖锐特性方面具有明显的改进。
