The convergence of object dependent resolution in maximum likelihood based tomographic image reconstruction

Area of Science:

• Medical imaging
• Image reconstruction algorithms
• Quantitative image analysis

Background:

• Image quality in medical imaging is critically dependent on reconstruction algorithms.
• Filtered backprojection (FBP) is a standard linear algorithm, while maximum likelihood (ML) is a nonlinear iterative algorithm.
• Comparing reconstruction algorithms necessitates standardized methods for assessing image resolution.

Purpose of the Study:

• To define and evaluate novel metrics for quantifying image resolution in nonlinear reconstruction algorithms.
• To compare the resolution characteristics of ML and FBP algorithms.
• To establish guidelines for matching resolution between ML and FBP for accurate comparisons.

Main Methods:

• Development of effective local Gaussian resolution (ELGR) and effective global Gaussian resolution (EGGR) metrics.
• Application of ELGR and EGGR to images reconstructed using FBP and ML algorithms.
• Analysis of resolution behavior with varying object sizes, iteration counts, and regularization parameters in ML.

Main Results:

• For FBP, ELGR and EGGR are equivalent and follow linear system behavior.
• For ML, ELGR is dependent on object size and convergence rate, particularly for smaller objects.
• EGGR for ML converges after approximately 200 iterations, potentially masking unresolved local details (ELGR).

Conclusions:

• Effective Gaussian resolution metrics (ELGR, EGGR) are crucial for comparing nonlinear ML with linear FBP.
• Matching EGGR between ML and FBP may require significantly more iterations than typically used for minimizing error.
• For accurate comparisons, especially with small objects, ensuring ELGR convergence in ML is essential and may necessitate >200 iterations.