3-D reconstruction from projections based on dynamic object models

An estimation approach to three dimensional reconstruction from projections, with incomplete and very noisy data, is suggested. Using a stochastic dynamic model for the object of interest in the probed domain, the reconstruction problem is reformulated as a nonlinear state estimation problem of small dimensionality, and an approximate MMSE globally optimal algorithm for its solution is presented. The algorithm, which is recursive in a hybrid frequency-space domain, operates directly on the Fourier transformed projection data, eliminating altogether the attempt to invert the projection integral equation. The computational requirements compare favorably with those of conventional reconstruction procedures, which fail in the limited and noisy data case.