Bayesian Nonparametric Dictionary Learning for Compressed Sensing MRI

TL;DR

This paper introduces a Bayesian nonparametric dictionary learning approach for improved MRI reconstruction from undersampled data, combining total variation regularization and stochastic optimization to enhance image quality.

Contribution

It develops a novel Bayesian nonparametric model with a data-driven dictionary learning prior tailored for MRI reconstruction, integrating total variation and efficient algorithms.

Findings

Improved MRI reconstruction accuracy over existing methods.

Effective removal of regularization parameter dependence in noisy settings.

Demonstrated success on multiple MRI datasets.

Abstract

We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and the patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov Chain Monte Carlo (MCMC) for the Bayesian model, and use the alternating direction method of multipliers (ADMM) for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.