# Model-based multi-parameter mapping

arXiv: https://arxiv.org/abs/2102.01604 · HTML: https://mlsanity.com/paper/2102.01604/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 84 references that are in the map.
- First posted on arXiv 2 Feb 2021.

## Builds on (most cited first, 9 of 9)

- [Convolutional Dictionary Learning: Acceleration and Convergence](https://mlsanity.com/paper/1707.00389/) (2017)
- [Direct Estimation of Spinal Cobb Angles by Structured Multi-Output Regression](https://mlsanity.com/paper/2012.12626/) (2020)
- [Flexible Bayesian Modelling for Nonlinear Image Registration](https://mlsanity.com/paper/2006.02338/) (2020)
- [MRI Super-Resolution using Multi-Channel Total Variation](https://mlsanity.com/paper/1810.03422/) (2018)
- [The divergence of the BFGS and Gauss Newton Methods](https://mlsanity.com/paper/1309.7922/) (2013)
- [An Algorithm for Learning Shape and Appearance Models without Annotations](https://mlsanity.com/paper/1807.10731/) (2018)
- [Empirical Bayesian Mixture Models for Medical Image Translation](https://mlsanity.com/paper/1908.05926/) (2019)
- [Joint Total Variation ESTATICS for Robust Multi-Parameter Mapping](https://mlsanity.com/paper/2005.14247/) (2020)
- [Fast T2 Mapping with Improved Accuracy Using Undersampled Spin-echo MRI and Model-based Reconstructions with a Generating Function](https://mlsanity.com/paper/1405.3574/) (2014)

## Built on by (most cited first, 1 of 1)

- [Correcting inter-scan motion artefacts in quantitative R1 mapping at 7T](https://mlsanity.com/paper/2108.10943/) (2021)

## Abstract (arXiv)

Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2*) or magnetisation-transfer saturation (MTsat), involves inverting a highly non-linear function. Many methods for deriving parameter maps assume perfect measurements and do not consider how noise is propagated through the estimation procedure, resulting in needlessly noisy maps. Instead, we propose a probabilistic generative (forward) model of the entire dataset, which is formulated and inverted to jointly recover (log) parameter maps with a well-defined probabilistic interpretation (e.g., maximum likelihood or maximum a posteriori). The second order optimisation we propose for model fitting achieves rapid and stable convergence thanks to a novel approximate Hessian. We demonstrate the utility of our flexible framework in the context of recovering more accurate maps from data acquired using the popular multi-parameter mapping protocol. We also show how to incorporate a joint total variation prior to further decrease the noise in the maps, noting that the probabilistic formulation allows the uncertainty on the recovered parameter maps to be estimated. Our implementation uses a PyTorch backend and benefits from GPU acceleration. It is available at https://github.com/balbasty/nitorch.