Hybrid regularization for mri reconstruction with static field inhomogeneity correction

Rapid acquisition of magnetic resonance (MR) images via reconstruction from undersampled k-space data has the potential to greatly decrease MRI scan time on existing medical hardware. To this end iterative image reconstruction based on the technique of compressed sensing has become the method choice for many researchers [1]. However, while conventional compressed sensing relies on random measurements from a discrete Fourier transform, actual MR scans often suffer from off-resonance effects and thus generate data by way of a non-Fourier operator, complicating image reconstruction methods and introducing additional computational bottlenecks [2]. In this work we introduce a combined TV-framelet regularization to the undersampled MR reconstruction problem in inhomogeneous fields. We show that the inclusion of a framelet regularization term decreases computation time and improves image quality over the traditional total variation (TV)-based approach.