SEARCHLIGHT CT: A NEW REGULARIZED RECONSTRUCTION METHOD FOR HIGHLY COLLIMATED X-RAY TOMOGRAPHY

This thesis introduces a new method for image reconstruction in collimated Computed Tomography called Searchlight CT. The method significantly reduces the overall radiation exposure when primarily the reconstruction of a specified region of interest is required. To achieve this, the Searchlight CT approach restricts the acquisition essentially to the region of interest, yet the algorithm provides a stable and robust reconstruction of the region of interest. The algorithm uses an iteration of the X-ray Transform and its regularized inverse. The performance of the algorithm is illustrated on simulated phantoms as well as experimental data. It is tested initially on 2D data and studied in detail for the 3D case including the adaptation to spiral tomography. Various methods of regularization are explored with special a emphasis on wavelet-based non-linear regularization. Finally the sensitivity of the algorithm to noise is studied. Numerical results for all cases are provided. The outline of an analytical proof for the convergence conditions is provided. The convergence is validated by the computation of the spectral radius of the iteration operator in various cases. A detailed analysis of the eigenvalues and eigenvectors leads to an apriori condition on convergence.Mathematics, Department o