New methods of image reconstruction: Convergence assurance, acceleration and convergent significance-weighted convolution

Computerised Tomography (CT) has singularly revolutionized the field of diagnostic medicine. CT produces cross sectional images of the human body without any invasive procedure. The process of producing these images is called reconstruction. There are, to date, two general classes of reconstruction algorithms. They are Algebraic methods and Convolution based methods. These algorithms produce these images from the projections of the cross section. A projection is a shadow image of the cross section. The criteria for judging the performance of a reconstruction algorithm are speed, amount of data (projections) and quality of the reconstructed image. Algebraic methods produce better images, but requires multiple iterations. This causes them to be slow, and the iterative nature of their implementation demands that they have convergent properties. There exists no definite criteria for convergence, and, in fact, Algebraic methods show tendencies to diverge. Thus speed, and convergence become an issue for iterative Algebraic methods. Convolution methods, on the other hand yield images in a single shot (very fast). But they tend to require much more data than Algebraic methods.;The main focus of this dissertation is to design reconstruction algorithms that combine the advantages of the above two classes. A criterion for convergence is derived, and a method of designing multiple acceleration parameters for iterative Algebraic methods is presented. Finally, the Convergent Significance-Weighted Convolution method, with the advantages of both Algebraic and Convolution methods is designed. Applications to the limited angle problem is studied. Extention to three dimensional reconstruction theory is discussed.