Iterative reconstruction-reprojection and the expectation-maximization algorithm.

The iterative reconstruction-reprojection (IRR) algorithm is a method for estimating missing projections in computed tomography. It is derived as an expectation-maximization (EM) algorithm that increases a suitable likelihood function. The constraint that the data form a consistent set of projections is loosened to require only that the means of the data form a consistent set, thereby suggesting that the algorithm is suitable for use with noisy data. Proofs of convergence to a stationary point and of monotonicity of the sequence of iterates are given. Simulations supporting these results are described.