Incorporating a Spatial Prior into Nonlinear D-Bar EIT imaging for Complex Admittivities

TL;DR

This paper introduces a novel 2-D D-bar EIT imaging method that incorporates spatial prior information to improve reconstruction quality of complex admittivities, especially under noisy conditions.

Contribution

It extends the D-bar method by integrating spatial priors into the scattering transform and D-bar equations, enhancing noise robustness and resolution in EIT imaging.

Findings

Improved reconstruction of chest phantoms with simulated pathologies.

Significant enhancement of pathology features despite high noise levels.

No prior pathology assumptions were needed for the prior data.

Abstract

Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filter to include higher frequency components in the reconstruction, in particular, features that are known with high confidence. This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.