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

8 May 2025
Chin-Cheng Chan
Justin P. Haldar
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Abstract

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, periodicity, 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).

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@article{chan2025_2505.05647,
  title={ A New k-Space Model for Non-Cartesian Fourier Imaging },
  author={ Chin-Cheng Chan and Justin P. Haldar },
  journal={arXiv preprint arXiv:2505.05647},
  year={ 2025 }
}
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