@MASTERSTHESIS\{IMM2015-07019,
    author       = "C. B. Hildebrandt",
    title        = "Linearized Acousto-Electric Impedance Tomography",
    year         = "2015",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Richard Petersens Plads, Building 324, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "{DTU} supervisor: Kim Knudsen, kiknu@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "The purpose of the thesis is to investigate the linearisation of Acousto-Electric Impedance Tomography as well as explaining the behaviour and characteristics of the reconstructions by use of singular value decomposition.

The thesis consists of an introduction to the model of Acousto-electric Impedance Tomography followed by a linearisation of the model by use of Fr\'{e}chet derivatives.  In order to do analysis of the system for the reconstruction the linearisation is then decoupled.  The system is implemented numerically in Python using FEniCS, [1],  to create reconstructions.  To improve the reconstructions Tikhonov regularization is introduced as well as truncated singular value decomposition to get rid of artefacts appearing in the reconstructions. The concept of noisy measurements is also investigated by adding Gaussian  noise  to  the  electrical  power  density  distribution,  where  we  again  get improved reconstructions by use of regularization.

To  examine  the  effectiveness,  when  access  to  the  boundary  is  restricted,  we  investigate what happens with the reconstructions when part of the boundary is set to have a homogeneous Dirchlet boundary condition.  Here it is clear that areas close to these boundaries gives unreliable reconstruction and we need regularization to get better solutions.  However when doing regularization we lose information about the unreliable areas and when we have elements hidden behind each other these are lost before the artefacts are removed."
}