Model-based multi-parameter mapping

Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, extracting quantitative parameters such as the longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2*), or magnetisation-transfer saturation (MTsat) involves inverting a highly non-linear function. Estimations often assume noise-free measurements and use subsets of the data to solve for different quantities in isolation, with error propagating through each computation. Instead, a probabilistic generative model of the entire dataset can be formulated and inverted to jointly recover parameter estimates with a well-defined probabilistic meaning (e.g., maximum likelihood or maximum a posteriori). In practice, iterative methods must be used but convergence is difficult due to the non-convexity of the log-likelihood; yet, we show that it can be achieved thanks to a novel approximate Hessian and, with it, reliable parameter estimates obtained. Here, we demonstrate the utility of this flexible framework in the context of the popular multi-parameter mapping framework and further show how to incorporate a denoising prior and predict posterior uncertainty. Our implementation uses a PyTorch backend and benefits from GPU acceleration. It is available at https://github.com/balbasty/nitorch.