# A New k-Space Model for Non-Cartesian Fourier Imaging

arXiv: https://arxiv.org/abs/2505.05647 · HTML: https://mlsanity.com/paper/2505.05647/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 66 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 6 of 6)

- [A multispeaker dataset of raw and reconstructed speech production real-time MRI video and 3D volumetric images](https://mlsanity.com/paper/2102.07896/) (2021)
- [cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs](https://mlsanity.com/paper/2102.08463/) (2021)
- [A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI](https://mlsanity.com/paper/2303.02586/) (2023)
- [CG-SENSE revisited: Results from the first ISMRM reproducibility challenge](https://mlsanity.com/paper/2008.04308/) (2020)
- [Linear Predictability in MRI Reconstruction: Leveraging Shift-Invariant Fourier Structure for Faster and Better Imaging](https://mlsanity.com/paper/1903.03141/) (2019)
- [Shannon-like Interpolation with Spectral Priors and Weighted Hilbert Spaces: Beyond the Nyquist Rate](https://mlsanity.com/paper/2410.21184/) (2024)

## Abstract (arXiv)

For the past several decades, it has been popular to reconstruct Fourier imaging data using model-based approaches that can easily incorporate physical constraints and advanced regularization/machine learning priors. The most common modeling approach is to represent the continuous image as a linear combination of shifted "voxel" basis functions. Although well-studied and widely-deployed, this voxel-based model is associated with longstanding limitations, including high computational costs, slow convergence, and a propensity for artifacts. In this work, we reexamine this model from a fresh perspective, identifying new issues that may have been previously overlooked (including undesirable approximation, wrap-around, and nullspace characteristics). Our insights motivate us to propose a new model that is more resilient to the limitations (old and new) of the previous approach. Specifically, the new model is based on a Fourier-domain basis expansion rather than the standard image-domain voxel-based approach. Illustrative results, which are presented in the context of non-Cartesian MRI reconstruction, demonstrate that the new model enables improved image quality (reduced artifacts) and/or reduced computational complexity (faster computations and improved convergence).