Three-dimensional reconstruction from projections with incomplete and noisy data by object estimation

An estimation approach to three-dimensional reconstruction from parallel ray projections, with incomplete and very noisy data, is described. Using a stochastic dynamic model for an object of interest in a probed domain of known background density, the reconstruction problem is reformulated as a nonlinear state estimation problem. An approximate minimum mean square error, globally optimal algorithm for the solution of this problem is presented. The algorithm, which is recursive in a hybrid frequency-space domain, operates directly on the Fourier-transformed projection data, eliminating the attempt to invert the projection integral equation. The simulation example considered demonstrates that good object estimates may be obtained with as few as five views in a limited sector of 90 degree and at a signal-to-noise ratio as low as 0 dB.