An efficient ADMM-based sparse reconstruction strategy for multi-level sampled MRI

Sparsity-driven image reconstruction is a promising paradigm for improving the spatial, temporal, and contrast resolution in magnetic resonance imaging (MRI). However, high computational expense continues to inhibit the translation of these techniques into routine clinical practice. In many MRI acquisition protocols (e.g., time-resolved CAPR), the sampling operator can be factored into a uniform and non-uniform component. In this work, we present a novel alternating direction method-of-multipliers (ADMM) strategy for sparse reconstruction of multilevel sampled Cartesian SENSE-type MRI data, and discuss how this framework enables certain operations to be computed once offline and recycled during the reconstruction process rather than repeated at every iteration. We then demonstrate that this algorithmic framework enables sparse reconstruction of 3D contrast-enhanced MR angiogram (CE-MRA) time-series in just several minutes (which is clinically practical) rather than the several hours previously required.