2D and 3D reconstructions in acousto-electric tomography

Peter Kuchment; Leonid Kunyansky

doi:10.1088/0266-5611/27/5/055013

2D and 3D reconstructions in acousto-electric tomography

Peter Kuchment, Leonid Kunyansky

Research output: Contribution to journal › Article › peer-review

58 Scopus citations

Abstract

We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the object with acoustic waves that slightly perturb the conductivity and cause the change in the electric potential measured on the boundary of the object. These perturbations of the potential are then used as the data for the reconstruction of the conductivity. The present method does not rely on 'perfectly focused' acoustic beams. Instead, more realistic propagating spherical fronts are utilized, and then the measurements that would correspond to perfect focusing are synthesized. In other words, we use synthetic focusing. Numerical experiments with simulated data show that our techniques produce high-quality images, both in 2D and 3D, and that they remain accurate in the presence of high-level noise in the data. Local uniqueness and stability for the problem also hold. © 2011 IOP Publishing Ltd.

Original language	English (US)
Pages (from-to)	055013
Journal	Inverse Problems
Volume	27
Issue number	5
DOIs	https://doi.org/10.1088/0266-5611/27/5/055013
State	Published - Apr 18 2011
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The work of both the authors was partially supported by the NSF DMS grant 0908208; the paper was written while they were visiting MSRI. The work of PK was also partially supported by the NSF DMS grant 0604778 and by the Award no KUS-C1-016-04, made to IAMCS by the King Abdullah University of Science and Technology (KAUST). The authors express their gratitude to NSF, MSRI, KAUST, and IAMCS for the support. Thanks also go to G Bal, E Bonnetier, J McLaughlin, L V Nguyen, L Wang, and Y Xu for helpful discussions and references. Finally, we are grateful to the referees for suggestions and comments that helped to significantly improve the paper.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1088/0266-5611/27/5/055013

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title = "2D and 3D reconstructions in acousto-electric tomography",

abstract = "We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the object with acoustic waves that slightly perturb the conductivity and cause the change in the electric potential measured on the boundary of the object. These perturbations of the potential are then used as the data for the reconstruction of the conductivity. The present method does not rely on 'perfectly focused' acoustic beams. Instead, more realistic propagating spherical fronts are utilized, and then the measurements that would correspond to perfect focusing are synthesized. In other words, we use synthetic focusing. Numerical experiments with simulated data show that our techniques produce high-quality images, both in 2D and 3D, and that they remain accurate in the presence of high-level noise in the data. Local uniqueness and stability for the problem also hold. {\textcopyright} 2011 IOP Publishing Ltd.",

author = "Peter Kuchment and Leonid Kunyansky",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The work of both the authors was partially supported by the NSF DMS grant 0908208; the paper was written while they were visiting MSRI. The work of PK was also partially supported by the NSF DMS grant 0604778 and by the Award no KUS-C1-016-04, made to IAMCS by the King Abdullah University of Science and Technology (KAUST). The authors express their gratitude to NSF, MSRI, KAUST, and IAMCS for the support. Thanks also go to G Bal, E Bonnetier, J McLaughlin, L V Nguyen, L Wang, and Y Xu for helpful discussions and references. Finally, we are grateful to the referees for suggestions and comments that helped to significantly improve the paper. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Kunyansky, Leonid

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N2 - We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the object with acoustic waves that slightly perturb the conductivity and cause the change in the electric potential measured on the boundary of the object. These perturbations of the potential are then used as the data for the reconstruction of the conductivity. The present method does not rely on 'perfectly focused' acoustic beams. Instead, more realistic propagating spherical fronts are utilized, and then the measurements that would correspond to perfect focusing are synthesized. In other words, we use synthetic focusing. Numerical experiments with simulated data show that our techniques produce high-quality images, both in 2D and 3D, and that they remain accurate in the presence of high-level noise in the data. Local uniqueness and stability for the problem also hold. © 2011 IOP Publishing Ltd.

AB - We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the object with acoustic waves that slightly perturb the conductivity and cause the change in the electric potential measured on the boundary of the object. These perturbations of the potential are then used as the data for the reconstruction of the conductivity. The present method does not rely on 'perfectly focused' acoustic beams. Instead, more realistic propagating spherical fronts are utilized, and then the measurements that would correspond to perfect focusing are synthesized. In other words, we use synthetic focusing. Numerical experiments with simulated data show that our techniques produce high-quality images, both in 2D and 3D, and that they remain accurate in the presence of high-level noise in the data. Local uniqueness and stability for the problem also hold. © 2011 IOP Publishing Ltd.

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2D and 3D reconstructions in acousto-electric tomography

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