Reconstruction algorithms for limited view projection data

Polar periodicities associated with the Radon transform and Lagrange multipliers are studies to obtain the sample/ recovery relationships. By considering a window function, which is zero outside the object boundaries and inside its transparent areas, a Fourier domain algorithm is introduced in which the Lagrange multipliers are determined using the window as a constraint. By expressing the backprojection image using the basis function of the projection transform a reconstruction model for fan beam projections is given. A very fast, iterative, space domain algorithm for divergent ray projections is introduced which gives the minimum energy reconstruction by exploiting a special matrix structure; this method matches the noise statistics and can utilise ´a priori´ knowledge.