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Combining Model Driven and Data Driven Approaches for Inverse Problems in Parameter Estimation and Image Reconstruction: From Modelling to Validation

Thomas Yu

Machine learning has become the state of the art for the solution of the diverse inverse problems arising from computer vision and medical imaging, e.g. denoising, super-resolution, de-blurring, reconstruction from scanner data, quantitative magnetic resonance imaging, etc, largely replacing the variational solutions of regularized optimization problems. However, between the two extremes of purely model-driven solutions, such as the solution of regularized optimization problems, and purely data-driven solutions, such as supervised deep learning, exist hybrid methods which combine aspects of both model-driven and data-driven solutions. Such hybrid methods are as manifold as the number of different inverse problems, as the particular characteristics of the inverse problem, e.g. availability of training data, complexity of the forward model, prior knowledge on solutions, etc., will understandably have a huge impact on the structure as well as the underlying techniques of the hybrid method. Furthermore, the validation of such approaches is also of utmost importance, particularly in medical imaging, where there are stringent requirements on the reliability of methods. In particular, hybrid methods are important when large, realistic training datasets are unavailable, such that one cannot immediately apply standard data-driven algorithms. In this thesis, we examine the solution and validation of four inverse problems derived from Magnetic Resonance Imaging (MRI) and computer vision, where we address the lack of large, realistic training datasets through solutions which try to maximally take advantage of the available model-driven and data-driven resources. We first show that self-supervised learning embedded in traditional model-driven schemes can be used to robustly solve inverse problems without ground-truth data. We conduct a rigorous validation of self-supervised methods for reconstructing MR images from raw measurement data through novel experiments on clinically relevant data, showing the importance of correct formulation of the forward model/conformity to the training data for image reconstruction quality, critically examining commonly used metrics for quantitative evaluation, and the generalization capabilities of self-supervised approaches. Furthermore, we propose embedding a neural network into a Hamiltonian Markov Chain Monte Carlo (HMCMC) sampling scheme with a self-supervised loss which improves the robustness and accuracy of solutions to a joint diffusometry/relaxometry problem, with respect to state of the art methods. Complementarily, we show that embedding realistic modeling into standard supervised learning schemes can be used to accommodate the lack of realistic, ground truth data. We combine realistic models and priors to create an extensive synthetic dataset and train a multi-layer perceptron for reconstructing

T_2

spectra from MRI data which is more accurate, robust, and orders of magnitude less computationally expensive than the state of the art. Finally, we propose parametrizing an analytically infeasible albeit realistic downsampling model in single image super-resolution through a neural network and integrating it into arbitrary deep learning pipelines which were trained on data with an unrealistic downsampling model, achieving state of the art performance in real-world super-resolution.

EPFL2022

Slice Estimation in Diffusion MRI of Neonatal and Fetal Brains in Image and Spherical Harmonics Domains Using Autoencoders

Meritxell Bach Cuadra, Erick Jorge Canales Rodriguez, Gabriel Girard, Hamza Kebiri, Thomas Yu

Diffusion MRI (dMRI) of the developing brain can provide valuable insights into the white matter development. However, slice thickness in fetal dMRI is typically high (i.e., 3-5 mm) to freeze the in-plane motion, which reduces the sensitivity of the dMRI signal to the underlying anatomy. In this study, we aim at overcoming this problem by using autoencoders to learn unsupervised efficient representations of brain slices in a latent space, using raw dMRI signals and their spherical harmonics (SH) representation. We first learn and quantitatively validate the autoencoders on the developing Human Connectome Project pre-term newborn data, and further test the method on fetal data. Our results show that the autoencoder in the signal domain better synthesized the raw signal. Interestingly, the fractional anisotropy and, to a lesser extent, the mean diffusivity, are best recovered in missing slices by using the autoencoder trained with SH coefficients. A comparison was performed with the same maps reconstructed using an autoencoder trained with raw signals, as well as conventional interpolation methods of raw signals and SH coefficients. From these results, we conclude that the recovery of missing/corrupted slices should be performed in the signal domain if the raw signal is aimed to be recovered, and in the SH domain if diffusion tensor properties (i.e., fractional anisotropy) are targeted. Notably, the trained autoencoders were able to generalize to fetal dMRI data acquired using a much smaller number of diffusion gradients and a lower b-value, where we qualitatively show the consistency of the estimated diffusion tensor maps.

SPRINGER INTERNATIONAL PUBLISHING AG2022

Variability and reproducibility of multi-echo T2 relaxometry: Insights from multi-site, multi-session and multi-subject MRI acquisitions

Elena Beanato, Julia Brügger, Andéol Geoffroy Cadic-Melchior, Erick Jorge Canales Rodriguez, Alessandro Daducci, Elda Fischi Gomez, Gabriel Girard, Tom Hilbert, Friedhelm Christoph Hummel, Tobias Kober, Philipp Johannes Koch, Takuya Morishita, Chang-Hyun Park, Gian Franco Piredda, Marco Pizzolato, Jean-Philippe Thiran, Maximilian Jonas Wessel, Thomas Yu

Quantitative magnetic resonance imaging (qMRI) can increase the specificity and sensitivity of conventional weighted MRI to underlying pathology by comparing meaningful physical or chemical parameters, measured in physical units, with normative values acquired in a healthy population. This study focuses on multi-echo T2 relaxometry, a qMRI technique that probes the complex tissue microstructure by differentiating compartment-specific T2 relaxation times. However, estimation methods are still limited by their sensitivity to the underlying noise. Moreover, estimating the model's parameters is challenging because the resulting inverse problem is ill-posed, requiring advanced numerical regularization techniques. As a result, the estimates from distinct regularization strategies are different. In this work, we aimed to investigate the variability and reproducibility of different techniques for estimating the transverse relaxation time of the intra- and extra-cellular space (TIE2 ) in gray (GM) and white matter (WM) tissue in a clinical setting, using a multi-site, multi-session, and multi-run T2 relaxometry dataset. To this end, we evaluated three different techniques for estimating the T2 spectra (two regularized non-negative least squares methods and a machine learning approach). Two independent analyses were performed to study the effect of using raw and denoised data. For both the GM and WM regions, and the raw and denoised data, our results suggest that the principal source of variance is the inter-subject variability, showing a higher coefficient of variation (CoV) than those estimated for the inter-site, inter-session, and inter-run, respectively. For all reconstruction methods studied, the CoV ranged between 0.32 and 1.64%. Interestingly, the inter-session variability was close to the inter-scanner variability with no statistical differences, suggesting that TIE2 is a robust parameter that could be employed in multi-site neuroimaging studies. Furthermore, the three tested methods showed consistent results and similar intra-class correlation (ICC), with values superior to 0.7 for most regions. Results from raw data were slightly more reproducible than those from denoised data. The regularized non-negative least squares method based on the L-curve technique produced the best results, with ICC values ranging from 0.72 to 0.92.

2022

Combining Model Driven and Data Driven Approaches for Inverse Problems in Parameter Estimation and Image Reconstruction: From Modelling to Validation

Thomas Yu

T_2

EPFL2022