Provably convergent OSEM-like reconstruction algorithm for emission tomography

Ing-Tsung Hsiao; Anand Rangarajan; Gene R. Gindi

doi:10.1117/12.467144

9 May 2002 Provably convergent OSEM-like reconstruction algorithm for emission tomography

Ing-Tsung Hsiao, Anand Rangarajan, Gene R. Gindi

Proceedings Volume 4684, Medical Imaging 2002: Image Processing; (2002) https://doi.org/10.1117/12.467144
Event: Medical Imaging 2002, 2002, San Diego, California, United States

Abstract

We investigate a new, provably convergent OSEM-like (ordered-subsets expectation-maximization) reconstruction algorithm for emission tomography. The new algorithm, which we term C-OSEM (complete-data OSEM), can be shown to monotonically increase the log-likelihood at each iteration. The familiar ML-EM reconstruction algorithm for emission tomography can be derived in a novel way. One may write a single objective function with complete, incomplete data and the reconstruction variables as in the EM approach. But in the objective function approach, there is no E-step. Instead, a suitable alternating descent on the complete data and then the reconstruction variables results in two update equations that can be shown to be equivalent to the familiar EM algorithm. Hence, minimizing this objective becomes equivalent to maximizing the likelihood. We derive our C-OSEM algorithm by modifying the above approach to update the complete data only along ordered subsets. The resulting update equation is quite different from OSEM, but still retains the speed-enhancing feature of the updates due to the limited backprojection facilitated by the ordered subsets. Despite this modification, we are able to show that the objective function decreases at each iteration, and (given a few more mild assumptions regarding the number of fixed points) conclude that the C-OSEM algorithm provides a monotonic convergence toward the maximum likelihood solution. We simulated noisy and noiseless emission projection data, and reconstructed them using the ML-EM, and the proposed C-OSEM with 4 subsets. We also reconstruct the data using the OSEM method. Anecdotal results show that the C-OSEM algorithm is much faster than ML-EM though slower than OSEM.

Citation Download Citation

Ing-Tsung Hsiao, Anand Rangarajan, and Gene R. Gindi "Provably convergent OSEM-like reconstruction algorithm for emission tomography", Proc. SPIE 4684, Medical Imaging 2002: Image Processing, (9 May 2002); https://doi.org/10.1117/12.467144

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available