Robust Computed Tomography with Incomplete Data 
 Abstract  This thesis provides the theoretical background for analysing the illposedness of Xray tomography problems and uses this to analyse the special case of laminar tomography problems.
The first part of the thesis is devoted to describing the illposed characteristics of Xray tomography problems. For this purpose we show that the deconvolution problem is illposed. In particular we show that small high frequent perturbations in the values of the convolution can give arbitrarily large changes in solutions to the deconvolution problem. We then relate the standard mathematical model of Xray tomography, the Radon transform, to the deconvolution problem and show that the illposed properties are likely to carry over. Moreover, we show that the discretised mathematical model of Xray tomography also exhibit the same illposed properties.
In the second part of the thesis, we develop a method of analysing the solvability of an Xray tomography problem by considering how illposed it is. In particular we use the method to describe the illposed characteristics of several "toy" problems. Finally the work culminates by considering two cases of laminar tomography. Here it is shown, that the characteristics from some of the toy problems carry over to the laminar tomography problems.  Type  Bachelor thesis [Academic thesis]  Year  2015  Publisher  Technical University of Denmark, Department of Applied Mathematics and Computer Science  Address  Richard Petersens Plads, Building 324, DK2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk  Series  DTU Compute B.Sc.2015  Note  DTU supervisor: Per Christian Hansen, pcha@dtu.dk, DTU Compute, cosupervised by Professor Bill Lionheart, The University of Manchester  Electronic version(s)  [pdf]  Publication link  http://www.compute.dtu.dk/English.aspx  BibTeX data  [bibtex]  IMM Group(s)  Scientific Computing 
