Nonconvex image reconstruction via expectation propagation.

Area of Science:

• Medical Imaging
• Computational Science
• Applied Mathematics

Background:

• Tomographic image reconstruction is often framed as a Bayesian inference problem.
• Standard optimization methods struggle with non-concave priors common in realistic image features like smoothness or sharpness.

Purpose of the Study:

• To develop a novel method for reconstructing images from Radon projections.
• To address the intractability of maximizing posterior probability with non-concave priors.

Main Methods:

• Utilized expectation propagation (EP) to approximate intractable posteriors in Bayesian inference.
• Applied EP with simple, non-log-concave priors to image reconstruction from Radon projections.

Main Results:

• Expectation propagation demonstrated superior performance compared to state-of-the-art algorithms.
• The method achieved lower reconstruction errors and required less information per pixel.
• Identified critical information rates for error-free image recovery through simulations.

Conclusions:

• Expectation propagation offers an effective approach for tomographic image reconstruction, especially with non-concave priors.
• The technique enhances accuracy and data efficiency in image recovery tasks.
• Provides a framework for determining optimal data acquisition parameters for reliable reconstruction.