Accelerated coordinate descent methods for Bayesian reconstruction using ordered subsets of projection data

Soo-Jin Lee

doi:10.1117/12.402437

4 October 2000 Accelerated coordinate descent methods for Bayesian reconstruction using ordered subsets of projection data

Soo-Jin Lee

Author Affiliations +

Proceedings Volume 4121, Mathematical Modeling, Estimation, and Imaging; (2000) https://doi.org/10.1117/12.402437
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

The ordered subsets (OS) algorithm¹ has enjoyed considerable interest for accelerating the well-known EM reconstruction algorithm for emission tomography and has recently found widespread use in clinical practice. This is primarily due to the fact that, while retaining the advantages of EM, the OS-EM algorithm can be easily implemented by slightly modifying the existing EM algorithm. The OS algorithm has also been applied¹ with the one-step-late (OSL) algorithm,² which provides maximum a posteriori estimation based on Gibbs priors. Unfortunately, however, the OSL approach is known to be unstable when the smoothing parameter that weights the prior relative to the likelihood is relatively large. In this work, we note that the OS principle can be applied to any algorithm that involves calculation of a sum over project indices, and show that it can also be applied to a generalized EM algorithm with useful quadratic priors. In this case, the algorithm is given in the form of iterated conditional modes (ICM), which is essentially a coordinate-wise descent method, and provides a number of important advantages. We also show that, by scaling the smoothing parameter in a principled way, the degree of smoothness is reconstructed images, which appears to vary depending on the number of subsets, can be efficiently matched for different numbers of subsets. Our experimental results indicate that the OS-ICM algorithm along with the method of scaling the smoothing parameter provides robust results as well as a substantial acceleration.

Citation Download Citation

Soo-Jin Lee "Accelerated coordinate descent methods for Bayesian reconstruction using ordered subsets of projection data", Proc. SPIE 4121, Mathematical Modeling, Estimation, and Imaging, (4 October 2000); https://doi.org/10.1117/12.402437

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