ALGORITHMS FOR SUPERIORIZATION AND THEIR APPLICATIONS TO IMAGE RECONSTRUCTION

Algorithms for image reconstruction that use blobs as their basis functions produce generally better results than algorithms that use other basis functions such as pixels or voxels. However, the reconstructions suffer from a major drawback: Oscillations are seen in the vicinity of sharp density changes in the object to be reconstructed. The proposed research work is motivated by this problem and is intended to provide a framework for algorithms (for image reconstruction from projections) that produce superior reconstructions. Our initial work and preliminary results support our objective and show how algorithms can incorporate the idea of perturbations in order to achieve superiorization. We focus our attention on two classes of projection methods and provide convergence theorems for each. Our planned research aims at expanding these results and is directed towards overcoming, by the technique of superiorization, the oscillations seen near discontinuities when blobs are used as the basis functions in image reconstruction.