Posterior temperature optimized Bayesian models for inverse problems in medical imaging

Area of Science:

• Medical Imaging
• Computational Science
• Bayesian Inference

Background:

• Bayesian methods are valuable for inverse problems like tomographic reconstruction and image denoising.
• Prior distributions offer regularization but often lead to suboptimal posterior temperatures, limiting Bayesian approach potential.

Purpose of the Study:

• To develop an unsupervised Bayesian approach, POTOBIM, for optimizing inverse problems in medical imaging.
• To enhance reconstruction accuracy and uncertainty estimation by optimizing prior parameters and posterior temperature.

Main Methods:

• Utilized mean-field variational inference with a fully tempered posterior.
• Employed Bayesian optimization with Gaussian process regression to optimize prior parameters and posterior temperature.
• Evaluated on four diverse inverse tasks across multiple imaging modalities using public datasets.

Main Results:

• Optimized posterior temperature in POTOBIM demonstrated superior performance compared to non-Bayesian and unoptimized Bayesian methods.
• Achieved improved accuracy and uncertainty quantification through optimized prior distribution and posterior temperature.
• Showcased that hyperparameters can be effectively determined per task domain for reliable predictions.

Conclusions:

• POTOBIM offers a robust framework for improving medical imaging inverse problems.
• Well-tempered posteriors are crucial for calibrated uncertainty estimation, enhancing prediction reliability.
• The optimized Bayesian approach provides significant advancements in image reconstruction and analysis.