Resolving quantitative MRI model degeneracy in self-supervised machine learning

Quantitative MRI (qMRI) estimates tissue properties of interest from measured MRI signals. This process is conventionally achieved by model fitting, whose computational expense limits qMRI's clinical use, motivating recent development of machine learning-based methods. Self-supervised approaches are particularly popular as they avoid the pitfall of distributional shift that affects supervised methods. However, it is unknown how such methods behave if similar signals can result from multiple tissue properties, a common challenge known as model degeneracy. Understanding this is crucial for ascertaining the scope within which self-supervised approaches may be applied. To this end, this work makes two contributions. First, we demonstrate that model degeneracy compromises self-supervised approaches, motivating the development of mitigation strategies. Second, we propose a mitigation strategy based on applying appropriate constraining transforms on the output of the bottleneck layer of the autoencoder network typically employed in self-supervised approaches. We illustrate both contributions using the estimation of proton density fat fraction and $R_2^*$ from chemical shift-encoded MRI, an ideal exemplar due to its exhibition of degeneracy across the full parameter space. The results from both simulation and $\textit{in vivo}$ experiments demonstrate that the proposed strategy helps resolve model degeneracy.