Model-based estimation techniques for 3-D reconstruction from projections

Yoram Bresler, Jeffrey A. Fessler, Albert Macovski

Abstract: A parametric estimation approach to reconstruction from projections with incomplete and very noisy data is described. Embedding prior knowledge about “objects” in the probed domain and about the data acquisition process into stochastic dynamic models, we transform the reconstruction problem into a computationally challenging nonlinear state-estimation problem, where the objects' parametrized descriptions are to be directly estimated from the projection data. This paper is a review in a common framework and a comparative study of two distinct algorithms which were developed recently for the solution of this problem. The first, is an approximate, globally optimal minimum-meansquare-error recursive algorithm. The second is a hierarchical suboptimal Bayesian algorithm. Simulation examples demonstrate accurate reconstructions with as few as four views in a 135∘ sector, at an average signal to noise ratio of 0.6.