A Novel k-Space Model for Non-Cartesian Reconstruction

Motivation: In model-based non-Cartesian MRI, it is common to represent the continuous image as a linear combination of voxel basis functions. Although this voxel-based model is widely used, reconstruction methods that use this model frequently suffer from slow convergence, high computational cost per iteration, and susceptibility to artifacts. Goal(s): To develop a new image model that mitigates the issues of the voxel-based model. Approach: Based on new theoretical insights, we choose to represent the image using a linear basis expansion in k-space. Results: The proposed k-space model has better representation capacity and is associated with reduced artifact vulnerability and improved reconstruction speed. Impact: We identify previously-unknown issues with the most popular (decades-old) approach to model-based non-Cartesian MRI reconstruction, and propose a new modeling approach that resolves these issues and offers better modeling accuracy, reduced susceptibility to artifacts, and greater computational efficiency.