To systematically review the techniques that address undersampling artifacts in accelerated quantitative magnetic resonance imaging (qMRI).
Methods: A literature search was conducted using the Embase, Medline, Web of Science Core Collection, Coherence Central Register of Controlled Trials, and Google Scholar databases for studies, published before July 2022 proposing reconstruction techniques for accelerated qMRI. Studies are reviewed according to inclusion criteria, and included studies are categorized based on the methodology used. Results: A total of 292 studies included in the review are categorized. A technical overview of each category is provided, and the categories are described in a unified mathematical framework. The distribution of the reviewed studies over time, application domain, and parameters of interest is illustrated. Conclusion: An increasing trend in the number of articles that propose new techniques for accelerated qMRI reconstruction indicates the importance of acceleration in qMRI. The techniques are mostly validated for relaxometry parameters and brain scans. The categories of techniques are compared based on theoretical grounds, highlighting existing trends and potential gaps in the field.