Image Reconstruction by Splitting Expectation Propagation Techniques from Iterative Inversion

TL;DR

This paper introduces a novel image reconstruction method combining Expectation Propagation with Monte Carlo, MCMC, and ADMM techniques, demonstrating improved efficiency and image quality in Gamma-camera imaging over traditional MCMC.

Contribution

The paper presents an innovative approach integrating EP with MC, MCMC, and ADMM for efficient Bayesian image reconstruction, addressing intractability issues.

Findings

The proposed methods outperform pure MCMC in image quality.

The new approach is less computationally expensive.

It achieves better parameter estimation.

Abstract

Reconstructing images from downsampled and noisy measurements, such as MRI and low dose Computed Tomography (CT), is a mathematically ill-posed inverse problem. We propose an easy-to-use reconstruction method based on Expectation Propagation (EP) techniques. We incorporate the Monte Carlo (MC) method, Markov Chain Monte Carlo (MCMC), and Alternating Direction Method of Multiplier (ADMM) algorithm into EP method to address the intractability issue encountered in EP. We demonstrate the approach on complex Bayesian models for image reconstruction. Our technique is applied to images from Gamma-camera scans. We compare EPMC, EP-MCMC, EP-ADMM methods with MCMC only. The metrics are the better image reconstruction, speed, and parameters estimation. Experiments with Gamma-camera imaging in real and simulated data show that our proposed method is convincingly less computationally expensive than MCMC and produces relatively a better image reconstruction.