Constrained Optimization Algorithms for Divergent Ray Tomography

Abstract

Using the projections as constraints, the reconstruction of an object from its fan beam projections is formulated and solved as a problem in constrained optimization. First a general cost criterion is optimized and the result is applied to several specific criteria. This produces a number of relationships (models) between the image and the Lagrange multipliers introduced by the Euler-Lagrange method. Utilizing these models, the ART methods are extended to fan beam projections. A non-recursive algorithm which exploits the speed of the block fast Fourier transform is given and compared with an existing convolution algorithm. The projection slice theorem for divergent ray geometry is given by introducing a new transform, the Angular Projection Transform.