Henrik Garde: This PhD thesis comprises mathematical methods for determining spatial structures using a relatively new tomographic method, known as electrical impedance tomography (EIT).
EIT is a safe technology based on measurements of weak electric fields through electrodes placed on the surface of the object. The method is capable of reconstructing the entire 3D structure from the measured data. Applications are, among others, monitoring of lung function, addition to mammography in early detection of breast cancer, as well as non-destructive detection of cracks and structural damage in materials.
Henrik Garde has developed reconstruction methods that improve the contrast and resolution in the reconstructed structures. The new algorithms use prior knowledge about the structures, which is modelled and implemented in a computationally efficient manner. Furthermore, Henrik has generalized a known method, the so-called monotonicity method, to make use of more complicated and precise electrode models that reduce the modelling errors. Finally, during his PhD-studies, Henrik has developed new theory that explains why inhomogeneities far from the measurement boundary only can be determined with great uncertainty.
The methods used in the PhD-project are based on theory for regularization in inverse problems, partial differential equations, Sobolev spaces on manifolds, and distribution theory. Reconstruction methods and theoretical bounds are verified through numerical experiments in 2- and 3-dimensions, from both simulated test problems and from real measurements.
Henrik Garde’s PhD-project is part of the project High-Definition Tomography, which is financed by an Advanced Grant from ERC.
Effective start/end date 01/03/2013 → 25/05/2016
Published as PhD report: Prior Information in Inverse Boundary Problems
Supervisor: Kim Knudsen
Section for Scientific Computing