Block-iterative Fisher scoring algorithms for maximum penalized likelihood image reconstruction in emission...

Area of Science:

• Medical Imaging
• Computational Science
• Statistical Modeling

Background:

• Tomographic reconstruction involves analyzing projection data with inherent Poisson variability.
• Regularized estimation is crucial for improving image quality and stability in such models.
• Existing algorithms may face challenges with nonnegatively constrained reconstructions.

Purpose of the Study:

• Introduce and evaluate a novel block-iterative Fisher scoring (BFS) algorithm.
• Assess the algorithm's convergence properties and its ability to handle Poisson noise.
• Compare the performance of the BFS algorithm against existing methods for constrained reconstruction.

Main Methods:

• Developed a block-iterative Fisher scoring (BFS) algorithm incorporating a general quadratic penalty for regularization.
• Proved local convergence of the BFS algorithm under specific conditions.
• Conducted simulation studies to evaluate convergence to both unconstrained and constrained maximum penalized likelihood (MPL) solutions.

Main Results:

• The BFS algorithm demonstrates local convergence without requiring iteration-dependent relaxation.
• Under suitable parameter choices and nonnegativity constraints, BFS converges to the constrained MPL solution.
• Constrained BFS frequently achieves the maximum penalized likelihood faster than alternative block-iterative algorithms.

Conclusions:

• The BFS algorithm provides an effective approach for regularized estimation in tomographic reconstruction with Poisson variability.
• The algorithm's proven convergence properties and efficiency in constrained scenarios make it a valuable tool.
• BFS offers a potentially faster and more stable reconstruction method for applications requiring nonnegativity constraints.