Limited angle reconstruction using stabilized algorithms

The stability of solutions to the limited-angle tomography reconstruction problem obtained by using the projections-onto-convex-sets (POCS) technique are examined. Although POCS techniques provide a feasible solution to the reconstruction problem, the solution is only one sample from the intersection of the closed convex sets that define the solution space. A method for evaluating the ensemble of possible solution waveforms that are in the neighborhood of a solution is presented. The ensemble characteristics are used to construct an inverse filter which is then applied to the computed solution. The results obtained using this method are less sensitive to noise amplification and are less dependent on both starting data and the number of iterations. An estimate of the object-dependent extrapolation that is possible using either linear or nonlinear constraints is provided.