On the convergence of an EM-type algorithm for penalized likelihood estimation in emission tomography

Area of Science:

• Statistical modeling
• Computational mathematics
• Image reconstruction

Background:

• The expectation maximization (EM) algorithm is widely used for parameter estimation in statistical models.
• Existing extensions of EM struggle with convergence proofs for certain regularization terms.
• Penalized likelihood estimation is crucial in fields like tomography for improving image quality.

Purpose of the Study:

• To present a generalized convergence result for the expectation maximization (EM) algorithm with regularization terms.
• To validate the applicability of the proposed method for penalized likelihood estimation in tomography.
• To establish a more robust theoretical foundation for EM algorithms incorporating penalty functions.

Main Methods:

• Development of a novel convergence proof for the expectation maximization (EM) algorithm.
• Analysis of the mathematical properties of continuous differentiability for penalty terms.
• Extension of the convergence result to other penalized likelihood estimation techniques.

Main Results:

• A simple convergence result is established for the expectation maximization (EM) algorithm with regularization.
• The proof requires only continuous differentiability of the penalty term, a less restrictive condition.
• The convergence result is shown to be extendable to other penalized likelihood methods in tomography.

Conclusions:

• The proposed convergence result significantly enhances the reliability of expectation maximization (EM) algorithms with regularization.
• This work provides a more broadly applicable theoretical framework for penalized likelihood estimation in complex inverse problems.
• The findings are particularly relevant for advancing image reconstruction techniques in medical imaging and other tomographic applications.