Fast EM-like methods for maximum "a posteriori" estimates in emission tomography

Area of Science:

• Medical Imaging
• Nuclear Medicine
• Image Reconstruction

Background:

• Maximum Likelihood (ML) and Filtered Backprojection (FBP) are common emission tomography reconstruction methods.
• Expectation-Maximization (EM) algorithm is iterative and popular for ML solutions due to its properties.
• Block sequential EM algorithms accelerate convergence by utilizing scanner geometry.

Purpose of the Study:

• To present an extension of the Relaxed Ordered Subsets Expectation-Maximization (RAMLA) algorithm for Maximum A Posteriori (MAP) reconstruction.
• To demonstrate that the extended RAMLA algorithm converges to the true MAP solution.
• To evaluate the performance of the extended RAMLA algorithm on simulated positron emission tomography data.

Main Methods:

• Extension of the RAMLA algorithm for MAP reconstruction.
• Theoretical analysis to show convergence to the true MAP solution.
• Application to simulated positron emission tomography data for performance comparison.

Main Results:

• The extended RAMLA algorithm is shown to converge to the true MAP solution.
• Experimental evidence supports the convergence of the algorithm.
• Comparison with the Ordered Subsets Gaussian Prior (OS-GP) method on simulated data.

Conclusions:

• The extended RAMLA algorithm provides a convergent approach for MAP image reconstruction in emission tomography.
• This method offers potential for improved image quality in emission tomography.
• Further validation and application to real-world data are warranted.