论文标题
使用直接反转D-bar和Calderon方法从电极数据中重建的3D EIT重建
3D EIT Reconstructions from Electrode Data using Direct Inversion D-bar and Calderon Methods
论文作者
论文摘要
提出了使用电极数据在3D中D-BAR方法的第一个数值实现。将结果与Calderón的方法以及更常见的电视和基于平滑度正则化的方法进行了比较。 D-BAR方法基于量身定制的非线性傅立叶变换，涉及测量的电流和电压数据。非线性傅里叶域中的低通滤波用于稳定重建过程。 D-BAR方法在2D中表现出很大的希望，可以提供可靠的实时绝对和时间差电导率重建，但尚未在3D中的实际电极数据上使用。为模拟数据提供了结果，以进行电导率和介电常数，并在球形域和嘈杂的电压数据上进行了非关节对称目标。证明3D D-BAR和Calderón方法可提供与2D CGO对应物相当的质量，并保持实时重建的希望。
The first numerical implementation of a D-bar method in 3D using electrode data is presented. Results are compared to Calderón's method as well as more common TV and smoothness regularization-based methods. D-bar methods are based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. D-bar methods have shown great promise in 2D for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D D-bar and Calderón methods are demonstrated to provide comparable quality to their 2D CGO counterparts, and hold promise for real-time reconstructions.
