Image Reconstruction from Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods

Previously unknown sufficient conditions, a necessary condition, and reconstruction methods for image reconstruction from cone-beam projections are developed. A sufficient condition developed is contained in the following statement. Statement 5: If one every plane that intersects the object, there exists at least one cone-beam source point, then the object can be reconstructed. Reconstruction methods for an arbitrary configuration of source points that satisfy Statement 5 are derived. By requiring additional conditions on the configuration of source points, a more efficient reconstruction method is developed. It is shown that when the configuration of source points is a circle, Statement 5 is not satisfied. In spite of this, several suggestions are made for reconstruction from a circle of source points.