Learning Compact <inline-formula> <tex-math notation="LaTeX">${q}$ </tex-math> </inline-formula>-Space Representations for Multi-Shell Diffusion-Weighted MRI

Abstract

Diffusion-weighted MRI measures the direction and scale of the local diffusion process in every voxel through its spectrum in q-space, typically acquired in one or more shells. Recent developments in microstructure imaging and multi-tissue decomposition have sparked renewed attention in the radial bvalue dependence of the signal. Applications in motion correction and outlier rejection therefore require a compact linear signal representation that extends over the radial as well as angular domain. Here, we introduce SHARD, a data-driven representation of the q-space signal based on spherical harmonics and a radial decomposition into orthonormal components. This representation provides a complete, orthogonal signal basis, tailored to the spherical geometry of q-space and calibrated to the data at hand. We demonstrate that the rank-reduced decomposition outperforms model-based alternatives in human brain data, whilst faithfully capturing the micro-and meso-structural information in the signal. Furthermore, we validate the potential of joint radialspherical as compared to single-shell representations. As such, SHARD is optimally suited for applications that require lowrank signal predictions, such as motion correction and outlier rejection. Finally, we illustrate its application for the latter using outlier robust regression.

Cross-scanner and cross-protocol multi-shell diffusion MRI data harmonization: Algorithms and results

“…Next, this method used the Spherical Harmonics and a Radial Decomposition (SHARD) proposed in ( Christiaens et al, 2018 ) as rotation-invariant representation of multi-shell dMRI data. SHARD learns the optimal low-rank representation of a given dataset (single subject or group), using a singular value decomposition across shells and spherical harmonic bands.…”

DIMOND: DIffusion Model OptimizatioN with Deep Learning

“…DIMOND's NN is optimized by minimizing the difference (e.g., mean squared error) between the raw acquired and synthesized image intensities ( I and $$\hat{\bm{I}}$$) using gradient descent within the mask where the diffusion model parameters are of interest. Constraints that leverage prior knowledge of the diffusion model (e.g., noise distribution, [ 43 ] sparsity, [ 44 ] low‐rankness [ 45 ] ) can be also incorporated into the loss function to further boost the performance. The modeling and optimization components of DIMOND vary across diffusion models and machine learning frameworks, which are therefore elaborated in the Experimental Section.…”

dStripe: slice artefact correction in diffusion MRI via constrained neural network

“…The dMRI data was processed using a motion correction and reconstruction algorithm (MCR) with integrated slice-to-volume reconstruction (SVR) (40). In brief, the reconstruction is based on an iterative estimation of a data-driven multi-shell low-rank (model-free) data representation (SHARD), slice outlier estimation, and rigid registration algorithm (41). The reconstruction utilises information from overlapping slices and the native slice profiles for super-resolution deconvolution and is formulated as an inverse problem that iteratively estimates the reconstruction coefficients x , defined in the motion-corrected “anatomical” space (the moving subject-aligned reference frame), and the rigid motion parameters μ that map between “source” space (the scattered slices in scanner coordinates) and anatomical space by minimising the difference between the acquired signal of a slice in the source space y s and its signal prediction The model consists of the q-space (SHARD) basis Q s ( μ s ), the linear motion and interpolation operator M ( μ s ), and the blurring and slice selection matrix B s that also incorporates the slice sensitivity profile.…”