Propagation of singularities for linearised hybrid data impedance tomography. (19th December 2017)

• Record Type: Journal Article
• Authors: Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim
• Is Part Of: Inverse problems. Volume 34:Number 2(2018:Feb.)
• Publication Date: 2017-12-19
• Subjects: hybrid data -- LSFEM -- reconstruction algorithm -- impedance tomography -- coupled physics tomograhy -- ultrasound modulated EIT -- acousto-electric tomography; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa9d78
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic conditions, and the associated directions of propagation are precisely identified relative to the directions in which ellipticity is lost. The same result is found in the setting for the corresponding normal formulation of the scalar pseudo-differential equations. A numerical reconstruction procedure based of the least squares finite element method is derived, and a series of numerical experiments visualise exactly how the loss of ellipticity manifests itself as propagating singularities.