Rethinking Model-Based Non-Cartesian Fourier Imaging: A New K-Space Model

Over the past quarter-century, model-based Fourier image reconstruction methods have typically modeled the continuous image as a linear combination of shifted voxel basis functions. Despite its popularity, this model suffers from long-standing practical issues (e.g., expensive computations and a propensity for artifacts). While substantial effort has been spent to alleviate these well-known problems, we observe in this work that this model also suffers from more fundamental issues that do not appear to be previously known. This includes an implicit periodicity assumption (which can limit modeling accuracy) and a systematic tendency to produce unrealistic cross-like structures in k-space. Importantly, we find that these issues can be effectively mitigated by replacing the image-domain model with a Fourier-domain model, leading to improved modeling accuracy, faster computations, and fewer artifacts. Results are demonstrated using non-Cartesian MRI data, although we expect our observations to be broadly relevant across all Fourier imaging modalities.