KAUST Grant NumberKUS-C1-016-04
MetadataShow full item record
AbstractWe 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.
CitationKuchment P, Kunyansky L (2011) 2D and 3D reconstructions in acousto-electric tomography. Inverse Problems 27: 055013. Available: http://dx.doi.org/10.1088/0266-5611/27/5/055013.
SponsorsThe 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.