A projection space map method for limited angle reconstruction

Jerry L. Prince, Alan S. Willsky

Abstract: Presents a method to reconstruct images from finite sets of noisy projections which are available only over limited or sparse angles. The method solves a constrained optimization problem to find a maximum a posteriori (MAP) estimate of the full 2-D Radon transform of the object, using prior knowledge of object mass, center of mass, and convex support, and information about fundamental constraints and smoothness of the Radon transform. This efficient primal-dual algorithm consists of an iterative local relaxation stage which solves a partial differential equation in Radon-space, followed by a simple Lagrange multiplier update stage. The object is reconstructed using convolution backprojection applied to the Radon transform estimate.< >