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Extension of emission expectation maximization lookalike algorithms to Bayesian algorithms
Gengsheng L Zeng1,2, Ya Li3
11Department of Engineering, Utah Valley University, 800 W University Parkway, Orem, UT 84058 USA.
Visual Computing for Industry, Biomedicine, and Art
|March 20, 2020
Summary
Researchers developed new Bayesian image reconstruction algorithms, extending existing ML-EM methods. These stable, efficient algorithms offer faster convergence and improved performance for emission and transmission tomography applications.
Area of Science:
- Medical Imaging
- Computational Science
Background:
- Maximum Likelihood Expectation Maximization (ML-EM) is a common iterative algorithm for image reconstruction.
- Existing ML-EM algorithms have limitations that can be addressed by incorporating Bayesian principles.
Purpose of the Study:
- To extend a family of ML-EM-like image reconstruction algorithms to Bayesian algorithms.
- To introduce a novel Bayesian extension applicable to both emission and transmission tomography.
Main Methods:
- Developed Bayesian algorithms by introducing a simple factor containing Bayesian information into multiplicative update schemes.
- Utilized the total-variation norm as a Bayesian constraint in computer simulations.
- Inspired by Green's one-step-late algorithm, but avoiding its undesirable step-size dependency.
Main Results:
- The newly developed Bayesian algorithms demonstrated stable performance in computer simulations.
- One algorithm is suitable for emission tomography, and another for transmission tomography.
- The algorithms exhibit multiplicative updating, non-negativity, and faster convergence for bright objects.
Conclusions:
- The extended Bayesian algorithms offer a stable and efficient alternative to existing methods.
- These algorithms are easily implemented and can be derived for any noise variance function.
- The proposed methods overcome limitations of previous algorithms, such as Green's algorithm's step-size dependency.
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