Reconstruction nonlinear full of images of electrical impedance tomography using the 2D D-bar method.

Author(s)

Miguel Fernando Montoya Vallejo

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Escola Politécnica (EP/BC)
• Defense date: 2012-10-16

Examining board members

Raúl González Lima; Joyce da Silva Bevilacqua; Antonio Carlos Gardel Leitão; Jennifer Lynn Mueller; Clodoaldo Grotta Ragazzo

• Advisor: Raúl González Lima; Jennifer Lynn Mueller

Abstract

This work proposes to develop a version of the D-bar method linearization for Electrical Impedance Tomography (EIT). The inverse problem of EIT is both nonlinear and very ill-posed. The version of the D-bar method implemented here is based on the existence and uniqueness proof of Adrian Nachman [Ann. of Math. 143 (1996)]. The method relies on the use of a nonlinear Fourier transform called the scattering transform, and the inherent ill-posedness of the inverse conductivity problem becomes evident in the computation of the scattering transform, more specifically in the determination of the Complex Geometrical Optics (CGO) solutions. Current practical implementations of the D-bar method using trigonometric patterns have replaced the boundary values of the CGO solutions by their asymptotic behavior in the calculation of the scattering transform, which is a linearization in this particular step of the overall method. This work proposes to calculate the scattering transform from exponentially growing solutions, which implies the calculation of the Faddeev Greens function, with the goal of obtaining images with higher resolution and accuracy in the conductivity values because the full nonlinear problem is solved. Numerical and experimental data using pairwise and trigonometric current injection patterns were used to evaluate the performance of the method. Better spatial resolution is obtained from the complete computation of the scattering transform. Reconstructed images from trigonometric current patterns also show better spatial resolution compared to pairwise current injection patterns, skipping three electrodes. (AU)

• FAPESP's process: 08/05951-5 - Full nonlinear 2D EIT D-bar reconstructions of Images for Electrical Impedance Tomography using the Method D-bar 2D
• Grantee: Miguel Fernando Montoya Vallejo
• Support Opportunities: Scholarships in Brazil - Doctorate