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

• URL: http://arxiv.org/abs/2505.05647v1
• Date: Thu, 08 May 2025 21:06:40 GMT
• Title: A New k-Space Model for Non-Cartesian Fourier Imaging
• Authors: Chin-Cheng Chan, Justin P. Haldar,
• Abstract summary: We propose a new model that is more resilient to the limitations (old and new) of the previous approach.<n>Specifically, the new model is based on a Fourier-domain basis expansion rather than the standard image-domain voxel-based approach.<n>Illustrative results are presented in the context of non-Cartesian MRI reconstruction.
• Score: 2.1730897280147814
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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