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Full-Text Articles in Mathematics
A Direct D-Bar Method For Partial Boundary Data Electrical Impedance Tomography With A Priori Information, Melody Alsaker, Sarah J. Hamilton, Andreas Hauptmann
A Direct D-Bar Method For Partial Boundary Data Electrical Impedance Tomography With A Priori Information, Melody Alsaker, Sarah J. Hamilton, Andreas Hauptmann
Mathematics, Statistics and Computer Science Faculty Research and Publications
Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that uses surface electrical measurements to determine the internal conductivity of a body. The mathematical formulation of the EIT problem is a nonlinear and severely ill-posed inverse problem for which direct D-bar methods have proved useful in providing noise-robust conductivity reconstructions. Recent advances in D-bar methods allow for conductivity reconstructions using EIT measurement data from only part of the domain (e.g., a patient lying on their back could be imaged using only data gathered on the accessible part of the body). However, D-bar reconstructions suffer from a loss of sharp edges …
Incorporating A Spatial Prior Into Nonlinear D-Bar Eit Imaging For Complex Admittivities, Sarah J. Hamilton, Jennifer L. Mueller, Melody Alsaker
Incorporating A Spatial Prior Into Nonlinear D-Bar Eit Imaging For Complex Admittivities, Sarah J. Hamilton, Jennifer L. Mueller, Melody Alsaker
Mathematics, Statistics and Computer Science Faculty Research and Publications
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 …
A Hybrid Segmentation And D-Bar Method For Electrical Impedance Tomography, Sarah J. Hamilton, J. M. Reyes, Samuli Siltanen, X. Zhang
A Hybrid Segmentation And D-Bar Method For Electrical Impedance Tomography, Sarah J. Hamilton, J. M. Reyes, Samuli Siltanen, X. Zhang
Mathematics, Statistics and Computer Science Faculty Research and Publications
The regularized D-bar method for electrical impedance tomography (EIT) provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e., without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed, leading to a loss of edge distinction. In this paper, a novel method that combines a D-bar approach with the edge-preserving nature of total variation (TV) regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-enhanced D-bar …