3D ELECTRICAL IMPEDANCE TOMOGRAPHY RECONSTRUCTIONS FROM SIMULATED ELECTRODE DATA USING DIRECT INVERSION t
exp AND CALDERÓN METHODS.
INVERSE PROBLEMS AND IMAGING (SPRINGFIELD, MO.) 2021;
15:1135-1169. [PMID:
35173824 PMCID:
PMC8846426 DOI:
10.3934/ipi.2021032]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The first numerical implementation of a t exp method in 3D using simulated electrode data is presented. Results are compared to Calderón's method as well as more common TV and smoothness regularization-based methods. The t exp method for EIT is 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. In 2D, t exp methods have shown great promise 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 t exp and Calderón methods are demonstrated to provide comparable quality to their 2D counterparts, and hold promise for real-time reconstructions due to their fast, non-optimized, computational cost.
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