A comparison of alternating minimization and expectation maximization algorithms for single source gamma ray tomography

Lange and Carson (1984 J. Comput. Assist. Tomogr. 8 306–16) defined image reconstruction for transmission tomography as a maximum likelihood estimation problem and derived an expectation maximization (EM) algorithm to obtain the maximum likelihood image estimate. However, in the maximization step or M-step of the EM algorithm, an approximation is made in the solution which can affect the image quality, particularly in the case of domains with high attenuating material. O'Sullivan and Benac (2007 IEEE Trans. Med. Imaging 26 283–97) reformulated the maximum likelihood problem as a double minimization of an I-divergence to obtain a family of image reconstruction algorithms, called the alternating minimization (AM) algorithm. The AM algorithm increases the log-likelihood function while minimizing the I-divergence. In this work, we implement the AM algorithm for image reconstruction in gamma ray tomography for industrial applications. Experimental gamma ray transmission data obtained with a fan beam geometry gamma ray scanner, and simulated transmission data based on a synthetic phantom, with two phases (water and air) were considered in this study. Image reconstruction was carried out with these data using the AM and the EM algorithms to determine and quantitatively compare the holdup distribution images of the two phases in the phantoms. When compared to the EM algorithm, the AM algorithm shows qualitative and quantitative improvement in the holdup distribution images of the two phases for both the experimental and the simulated gamma ray transmission data.