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'.
Keywords: inverse problems; magnetic resonance imaging; model-based reconstruction.