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.

We propose a new method, Patch-CNN, for diffusion tensor (DT) estimation from only six-direction diffusion weighted images (DWI). Deep learning-based methods have been recently proposed for dMRI parameter estimation, using either voxel-wise fully-connected neural networks (FCN) or image-wise convolutional neural networks (CNN). In the acute clinical context -- where pressure of time limits the number of imaged directions to a minimum -- existing approaches either require an infeasible number of training images volumes (image-wise CNNs), or do not estimate the fibre orientations (voxel-wise FCNs) required for tractogram estimation. To overcome these limitations, we propose Patch-CNN, a neural network with a minimal (non-voxel-wise) convolutional kernel (3$\times$3$\times$3). Compared with voxel-wise FCNs, this has the advantage of allowing the network to leverage local anatomical information. Compared with image-wise CNNs, the minimal kernel vastly reduces training data demand. Evaluated against both conventional model fitting and a voxel-wise FCN, Patch-CNN, trained with a single subject is shown to improve the estimation of both scalar dMRI parameters and fibre orientation from six-direction DWIs. The improved fibre orientation estimation is shown to produce improved tractogram.