Conference paper · Preprint article
3D reconstruction for partial data electrical impedance tomography using a sparsity prior
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 ℓ1 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.
Language: | English |
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Publisher: | American Institute of Mathematical Sciences (AIMS) |
Year: | 2015 |
Pages: | 495-504 |
Proceedings: | 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (2014) |
Types: | Conference paper and Preprint article |
DOI: | 10.3934/proc.2015.0495 |
ORCIDs: | Knudsen, Kim |