The objective of this work is to derive the theoretical and numerical tools necessary for the development of computer algorithms for image reconstruction from cone- beam projections which are computationally efficient and accurate. In particular four tasks will be addressed. First, rigorous proofs of the reconstruction formulas derived formally in the preliminary research will be made. The rigorous proofs will give more credence to these formulas, possibly eliminate any oversights made in the formal derivations, and will result in a better conceptual understanding of the formulas involved. Developing the rigorous proofs will also provide a strong background for another task to be performed -- the development of quadratures. Fast and accurate quadratures are needed for computing the singular, spherical integrals which are involved in several cone--beam reconstruction formulas. Since complete information can not be measured from some date collection geometries that are mechanically simple to implement, another task to be addressed is the development of extrapolation methods that will help compensate for this lack of complete information. Closely related to the development of extrapolation methods is the task of development of extrapolation methods is the task of developing properties of an intermediate function which is being computed in several of the reconstruction methods. Properties of this intermediate function will be developed with the goal of improving the accuracy an speed of its computation.
