DeepMpMRI: Tensor-decomposition Regularized Learning for Fast and High-Fidelity Multi-Parametric Microstructural MR Imaging

TL;DR

DeepMpMRI tackles the ill-posed problem of simultaneously estimating multiple diffusion-derived microstructural parameters from sparse q-space data by introducing a tensor-decomposition-based regularizer that preserves high-order correlations across parameters. Coupled with a lightweight Nesterov-based adaptive learning algorithm, the framework dynamically tunes regularization strength, enabling efficient end-to-end learning with a flexible backbone (e.g., HGT). Empirical results on the HCP and Alzheimer's datasets show state-of-the-art accuracy and robust detail preservation, with 4.5–15× acceleration over dense sampling and strong resilience to noise. The work advances fast, high-fidelity multi-model diffusion MRI, with clear implications for clinically feasible microstructure imaging and biomarker discovery.

Abstract

Deep learning has emerged as a promising approach for learning the nonlinear mapping between diffusion-weighted MR images and tissue parameters, which enables automatic and deep understanding of the brain microstructures. However, the efficiency and accuracy in estimating multiple microstructural parameters derived from multiple diffusion models are still limited since previous studies tend to estimate parameter maps from distinct models with isolated signal modeling and dense sampling. This paper proposes DeepMpMRI, an efficient framework for fast and high-fidelity multiple microstructural parameter estimation from multiple models using highly sparse sampled q-space data. DeepMpMRI is equipped with a newly designed tensor-decomposition-based regularizer to effectively capture fine details by exploiting the high-dimensional correlation across microstructural parameters. In addition, we introduce a Nesterov-based adaptive learning algorithm that optimizes the regularization parameter dynamically to enhance the performance. DeepMpMRI is an extendable framework capable of incorporating flexible network architecture. Experimental results on the HCP dataset and the Alzheimer's disease dataset both demonstrate the superiority of our approach over 5 state-of-the-art methods in simultaneously estimating multi-model microstructural parameter maps for DKI and NODDI model with fine-grained details both quantitatively and qualitatively, achieving 4.5 - 15 $\times$ acceleration compared to the dense sampling of a total of 270 diffusion gradients.

Figures (13)

• Figure 1: Schematic illustration of DKI and NODDI-derived microstructural parameter correlation in the nerve cross-sectional anatomy.
• Figure 2: An illustration of the proposed DeepMpMRI framework. Left: The whole architecture consists of two branches, with the upper branch being the reference acquisition from the dense sampling and the lower branch being the network prediction from the sparse sampling. The input of the framework is sparse measurements uniformly sampled at each shell from the dense measurements, and tensor Singular Value Decomposition (t-SVD) is applied to both network prediction and reference to further align them on the tensor singular values to capture the correlation shared among multiple microstructural parameters. Right: The flowchart of tensor-SVD implementation. For detailed information, please refer to kolda2001orthogonalkolda2009tensorchen2009tensorkilmer2011factorizationlu2019tensor.
• Figure 3: The reference, estimated parameters (KFA, MK, AK, RK, OD, $V_{ic}$, $V_{iso}$) and corresponding error maps based on Model Fitting (MF), q_DL, U-Net, MESC-SD, and Ours in a test subject with 6 diffusion directions per shell at b-values of 1000, 2000, and 3000 $s/{mm}^2$.
• Figure 4: Quantitative comparison of different DL-based methods on the AD dataset. The results were obtained with 6 diffusion directions per shell at b-values of $1000,\ 2000,\ 3000s/{mm}^2$.
• Figure 5: Tract-based spatial statistics (TBSS) analysis revealed significant differences ($p < 0.05$) in multiple parameter values associated with changes in brain white matter for AD patients compared to healthy controls.