Fast 3D Partial Boundary Data EIT Reconstructions Using Direct Inversion CGO-Based Methods

To develop, and test, a fast image 3D reconstruction method for partial boundary data electrical impedance tomographic absolute and time-difference imaging.

Two complex geometrical optics based methods are presented: Calerón's method which employs a linear Fourier transform, and the $\operatorname{\mathbf {t}^{{{\mathbf{exp}}}}}$ method which makes use of a tailor-made nonlinear Fourier transform. The methods are tested on simulated and experimental data, and their reconstructions compared to reference reconstructions from standard linear difference imaging and total variation regularization.

The proposed methods provide good localization of targets, for both absolute and time-difference imaging, when large portions of the domain are inaccessible for measurement, e.g., stroke monitoring.

The proposed algorithms require no iteration and provide informative absolute or time-difference images exceptionally quickly in under 2 seconds for complicated domain shapes. The algorithms perform well under high levels of noise and incorrect domain modeling.

As most medical applications of electrical impedance tomography are limited to partial boundary data, the development of partial boundary algorithms is highly desirable. While iterative schemes have been used traditionally, their high computational cost can make them cost-prohibitive for applications that need fast imaging.