Conventional magnetic resonance imaging (MRI) is hampered by long scan times and only qualitative image contrasts that prohibit a direct comparison between different systems. To address these limitations, model-based reconstructions explicitly model the physical laws that govern the MRI signal generation. By formulating image reconstruction as an inverse problem, quantitative maps of the underlying physical parameters can then be extracted directly from efficiently acquired k-space signals without intermediate image reconstruction—addressing both shortcomings of conventional MRI at the same time. This review will discuss basic concepts of model-based reconstructions and report on our experience in developing several model-based methods over the last decade using selected examples that are provided complete with data and code.

This article is part of the theme issue ‘Synergistic tomographic image reconstruction: part 1’.

传统的磁共振成像 (MRI) 受到长扫描时间和仅定性图像对比度的限制，无法在不同系统之间进行直接比较。为了解决这些限制，基于模型的重建明确地模拟了控制 MRI 信号生成的物理定律。通过将图像重建表述为逆问题，可以直接从有效采集的 k 空间信号中提取基础物理参数的定量图，无需中间图像重建，同时解决了传统 MRI 的两个缺点。本综述将讨论基于模型的重建的基本概念，并报告我们在过去十年中使用提供完整数据和代码的选定示例开发几种基于模型的方法的经验。

本文是主题“协同断层扫描图像重建：第 1 部分”的一部分。