A hierarchical algorithm for limited-angle reconstruction

The authors describe and demonstrate a hierarchical reconstruction algorithm for use in noisy and limited-angle or sparse-angle tomography. The algorithm estimates the object´s mass, center of mass, and convex hull from the available projections, and uses this information, along with fundamental mathematical constraints, to estimate a full set of smoothed projections. The mass and center of mass are estimated using a maximum-likelihood (ML) estimator derived from the principles of consistency of the Radon transform. The convex hull estimate is produced by first estimating the positions of support lines of the object from each available projection and then estimating the overall convex hull using ML or maximum a posteriori (MAP) techniques. The position of two support lines from a single projection is estimated using either a generalized likelihood ratio technique for estimating jumps in linear systems or a support-width penalty method that uses Akaike´s model-order estimation technique