3D reconstruction for partial data electrical impedance tomography using a sparsity prior

Pages: 495 - 504, Issue special, November 2015

doi:10.3934/proc.2015.0495        Abstract        References        Full Text (2129.5K)              

Henrik Garde - Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark (email)
Kim Knudsen - Danmarks Tekniske Universitet, Department of Applied Mathematics and Computer Science, Matematiktorvet, Building 303 B, DK - 2800 Kgs. Lyngby, Denmark (email)

Abstract: In electrical impedance tomography the electrical conductivity inside a physical body is computed from electro-static boundary measurements. The focus of this paper is to extend recent results for the 2D problem to 3D: prior information about the sparsity and spatial distribution of the conductivity is used to improve reconstructions for the partial data problem with Cauchy data measured only on a subset of the boundary. A sparsity prior is enforced using the $\ell_1$ norm in the penalty term of a Tikhonov functional, and spatial prior information is incorporated by applying a spatially distributed regularization parameter. The optimization problem is solved numerically using a generalized conditional gradient method with soft thresholding. Numerical examples show the effectiveness of the suggested method even for the partial data problem with measurements affected by noise.

Keywords:  Impedance tomography, sparsity, partial data, prior information, numerical reconstruction.
Mathematics Subject Classification:  Primary: 65N20, 65N21.

Received: September 2014;      Revised: August 2015;      Published: November 2015.