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).

翻译：在过去的几十年中，基于模型的傅里叶成像数据重建方法因其易于融入物理约束和先进正则化/机器学习先验而广受欢迎。最常见的建模方法是将连续图像表示为平移"体素"基函数的线性组合。尽管这一基于体素的模型已被充分研究并广泛部署，但其固有局限性长期存在，包括计算成本高、收敛速度慢以及易产生伪影。本研究以全新视角重新审视该模型，识别出若干可能先前被忽视的新问题（包括不良近似、环绕效应及零空间特性）。这些发现促使我们提出一种对传统方法的既有及新局限性更具鲁棒性的新模型。具体而言，新模型基于傅里叶域基展开而非标准图像域体素方法。在非笛卡尔MRI重建背景下的示例结果表明，新模型能够提升图像质量（减少伪影）和/或降低计算复杂度（加速计算与改善收敛性）。