3D EIT Reconstructions from Electrode Data using Direct Inversion D-bar and Calderon Methods
The first numerical implementation of a D-bar method in 3D using electrode data is presented. Results are compared to Calderón's method as well as more common TV and smoothness regularization-based methods. D-bar methods are based on tailor-made non-linear Fourier transforms involving the measu...
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| Main Authors | , , , , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
06.07.2020
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2007.03018 |
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| Abstract | The first numerical implementation of a D-bar method in 3D using electrode
data is presented. Results are compared to Calderón's method as well as more
common TV and smoothness regularization-based methods. D-bar methods are 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. D-bar methods have shown great promise in
2D 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 D-bar and Calderón methods are demonstrated to
provide comparable quality to their 2D CGO counterparts, and hold promise for
real-time reconstructions. |
|---|---|
| AbstractList | The first numerical implementation of a D-bar method in 3D using electrode
data is presented. Results are compared to Calderón's method as well as more
common TV and smoothness regularization-based methods. D-bar methods are 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. D-bar methods have shown great promise in
2D 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 D-bar and Calderón methods are demonstrated to
provide comparable quality to their 2D CGO counterparts, and hold promise for
real-time reconstructions. |
| Author | Hamilton, Sarah J Kolehmainen, Ville Bray, Patrick F Isaacson, David Toivanen, Jussi Muller, Peter A |
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| BackLink | https://doi.org/10.48550/arXiv.2007.03018$$DView paper in arXiv |
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| Snippet | The first numerical implementation of a D-bar method in 3D using electrode
data is presented. Results are compared to Calderón's method as well as more
common... |
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| SubjectTerms | Computer Science - Numerical Analysis Mathematics - Analysis of PDEs Mathematics - Numerical Analysis |
| Title | 3D EIT Reconstructions from Electrode Data using Direct Inversion D-bar and Calderon Methods |
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