Showing papers on "Ordered subset expectation maximization published in 1993"

Comparison between ML-EM and modified Newton algorithms for SPECT image reconstruction

Abstract: The expectation maximization method for maximum likelihood image reconstruction (ML- EM) is one of the most popular algorithms used in SPECT and PET, because it is based on the realistic assumption that photon emission and counts follow a Poisson process. Moreover, this method retains two important theoretical and practical properties namely nonnegativity and self-normalization of the reconstructed image. This latter property means that the number of emitted photons is equal to the number of counts. However, the major disadvantage of this method is the large amount of computation that is required, due to its slow rate of convergence. In this paper, we demonstrate that the ML-EM algorithm is a special case of the modified Newton method and can thus be accelerated by multiplying at each iteration the changes to the image, as calculated by the standard algorithm, by an overrelaxation parameter. This accelerated ML-EM algorithm can further be optimally accelerated, and converges to a good maximum likelihood estimator.

A 3-D Filtered-Backprojection Reconstruction Algorithm for Combined Parallel- and Cone-Beam SPECT Data

Abstract: Cone-beam (cb) collimation for single-photon emission computed tomography (spect) provides higher sensitivity than parallel-hole collimation, however it produces truncated projection data that can lead to undesirable image artifacts. In response, it has been suggested (Jaszczak 1992) that parallel-beam and cone-beam data be combined to obtain increased sensitivity while maintaining completeness of the data for accurate reconstruction. Herein, a 3-d filtered-backprojection (fbp) approach for reconstructing such data sets is proposed. The algorithm begins with a rebinning of the parallel- and cone-beam (p&cb) data to a common planeintegral projection space: the projection space of the 3-d Radon transform. A normalization step is then implemented to correct for the sampling pattern of the system, thus assuring that the rebinned data are proportional to the plane integrals of the source distribution of the object. Finally, a fully 3-D fbp reconstruction based on the inversion formula of the 3-Radon transform is performed using the rebinned plane integrals. The advantage of this algorithm is that, by making the necessary corrections prior to reconstruction, it avoids residual artifacts that can remain after other methods are employed. In addition, the computation time required by the proposed method is substantially shorter than that reported for maximum-likelihood reconstructions by the expectation-maximization (em) algorithm (Jaszczak 1992).