Bayesian Nonparametric Dictionary Learning for Compressed Sensing MRI
This addresses compressed sensing MRI reconstruction for medical imaging applications, representing an incremental improvement through hybrid Bayesian optimization.
The authors tackled MRI reconstruction from undersampled data by developing a Bayesian nonparametric dictionary learning model that infers dictionary size and sparsity patterns from data, combined with total variation penalty. Their method improved reconstruction accuracy over other approaches in empirical tests on several MRI datasets.
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.