MRI Parameter Mapping via Gaussian Mixture VAE: Breaking the Assumption of Independent Pixels

TL;DR

A self-supervised deep variational approach that breaks the assumption of independent pixels, leveraging redundancies in the data to effectively perform data-driven regularisation of quantitative maps in MRI and can support the clinical adoption of parameter mapping methods such as dMRI and qMRI.

Abstract

We introduce and demonstrate a new paradigm for quantitative parameter mapping in MRI. Parameter mapping techniques, such as diffusion MRI and quantitative MRI, have the potential to robustly and repeatably measure biologically-relevant tissue maps that strongly relate to underlying microstructure. Quantitative maps are calculated by fitting a model to multiple images, e.g. with least-squares or machine learning. However, the overwhelming majority of model fitting techniques assume that each voxel is independent, ignoring any co-dependencies in the data. This makes model fitting sensitive to voxelwise measurement noise, hampering reliability and repeatability. We propose a self-supervised deep variational approach that breaks the assumption of independent pixels, leveraging redundancies in the data to effectively perform data-driven regularisation of quantitative maps. We demonstrate that our approach outperforms current model fitting techniques in dMRI simulations and real data. Especially with a Gaussian mixture prior, our model enables sharper quantitative maps, revealing finer anatomical details that are not presented in the baselines. Our approach can hence support the clinical adoption of parameter mapping methods such as dMRI and qMRI.

Figures (7)

• Figure 1: Diffusivity results on simulated model using MSDKI, comparisons between self-supervised baseline and our VAE-UniG. X axis: ground truth of simulated diffusivity. Y axis: prediction of diffusivity. SNR: signal-noise-ratio. Blue: cluster 1. Orange: cluster 2. Green: cluster 3. Ours vastly outperforms the baseline in recovery of the ground truth. See the kurtosis results in the appendix Fig.\ref{['fig:simulated_msdki_k']}.
• Figure 2: LSQ, self-supervised, VAE-UniG, VAE-GMM ball-stick fits to HCP dMRI subject. Both our VAE models drastically reduce noises (1st Row) for sharper white matter visulisation. More importantly, our VAE-GMM reveals finer anatomical structures with clear details which were not seen in the baselines (see the arrows locations in 3rd Row, 4th Col).
• Figure 3: Visualisation of the learnt posterior distributions of the latent variable $z$ training on HCP data. 1st row: VAE. 2nd row: GMM VAE.
• Figure 4: Architectures of our model implementations. Row 1: with univariate prior. Row 2: with Gaussian mixture model prior. The encoder is three fully connected layers. The decoder is one fully connected layer.
• Figure 5: Comparisons on MS-DKI fits on HCP dMRI subject. Our approach has less obvious improvements when the MRI model is relatively simple, but doesn't hallucinate spurious anatomical features.