Separation of Water Components from Multi-Echo MRI Data Using Deep Learning-Assisted Subspace Modeling

MRI data acquired using multi-echo spin-echo or gradient-echo sequences contain "encoded" water signals from various tissue compartments, i.e., myelin, axon, and extracellular space. Accurate separation of these components is desirable for tissue characterization in healthy and diseased states. However, this signal decomposition problem is very challenging because the encoding matrix is highly ill-conditioned and as a result, its solution is often sensitive to noise and practical data perturbations (e.g., B₀ field inhomogeneity). This paper presents a new method to address this problem, which synergistically integrates physics-based spatiotemporal priors and machine learning to constrain the variations allowed for each water component while providing flexibility to capture subject- and experiment-dependent signal changes. Specifically, we introduced a probabilistic union-of-subspaces model with pre-learned spectral bases to enforce temporal constraints while incorporating spatial priors derived from deep learning-based image translation. To further accommodate subject- and experiment-specific signal variations, a generalized series model was employed to adapt the pre-learned subspace model to a specific dataset. With the proposed model and learned priors, water separation was done under the Bayesian statistical framework. Numerical simulations and experimental evaluations demonstrated that the proposed method significantly improved the accuracy of the estimated myelin, axonal, and extracellular water components. The new method will enhance the practical utility of multi-component water imaging for basic neuroscience and clinical applications and also provide a useful framework for separating overlapping spatiotemporal signals.