The ML-EM Algorithm is Not Optimal for Poisson Noise.

Area of Science:

• Medical Imaging
• Computational Science
• Signal Processing

Background:

• Maximum Likelihood Expectation Maximization (ML-EM) is a widely used iterative algorithm for image reconstruction, particularly in scenarios with Poisson noise.
• ML-EM is known to converge to the true solution in early iterations but diverge in later stages.
• Early termination of ML-EM is often employed to obtain an approximate solution, but its optimality is questionable.

Purpose of the Study:

• To evaluate the optimality of the ML-EM algorithm for image reconstruction from noisy projection data.
• To determine if ML-EM can consistently provide approximate solutions close to the true solution.
• To introduce and validate an alternative algorithm that potentially outperforms ML-EM.

Main Methods:

• The study analyzes the convergence properties of the ML-EM algorithm.
• It investigates the limitations of early termination for ML-EM.
• A novel alternative iterative algorithm is proposed and compared against ML-EM.

Main Results:

• The ML-EM algorithm's convergence behavior shows a tendency to diverge from the true solution in later iterations.
• Early termination of ML-EM does not guarantee an optimal approximate solution.
• The proposed alternative algorithm demonstrates superior performance over ML-EM in image reconstruction tasks.

Conclusions:

• The ML-EM algorithm is not optimal for obtaining accurate approximate solutions in image reconstruction with noisy data.
• Alternative algorithms can outperform ML-EM, offering improved accuracy.
• Further research into advanced reconstruction algorithms is warranted for better image quality.