Equivariant Spherical Deconvolution: Learning Sparse Orientation Distribution Functions from Spherical Data

@inproceedings{Elaldi2021EquivariantSD,
  title={Equivariant Spherical Deconvolution: Learning Sparse Orientation Distribution Functions from Spherical Data},
  author={Axel Elaldi and Neel Dey and Heejong Kim and G. Gerig},
  booktitle={IPMI},
  year={2021}
}
We present a rotation-equivariant unsupervised learning framework for the sparse deconvolution of non-negative scalar fields defined on the unit sphere. Spherical signals with multiple peaks naturally arise in Diffusion MRI (dMRI), where each voxel consists of one or more signal sources corresponding to anisotropic tissue structure such as white matter. Due to spatial and spectral partial voluming, clinically-feasible dMRI struggles to resolve crossing-fiber white matter configurations, leading… Expand

Figures and Tables from this paper

Geometric Deep Learning and Equivariant Neural Networks
TLDR
The mathematical foundations of geometric deep learning is surveyed, focusing on group equivariant and gaugeEquivariant neural networks and the use of Fourier analysis involving Wigner matrices, spherical harmonics and Clebsch–Gordan coefficients for G = SO(3), illustrating the power of representation theory for deep learning. Expand

References

SHOWING 1-10 OF 22 REFERENCES
Diffusion MRI fiber orientation distribution function estimation using voxel-wise spherical U-net
Diffusion Magnetic Resonance Imaging (dMRI) is an imaging technique which enables analysis of the brain tissue at a microscopic scale, particularly the analysis of white matter. Given a high enoughExpand
Sparse wars: A survey and comparative study of spherical deconvolution algorithms for diffusion MRI
TLDR
Results from this exhaustive evaluation show that there is no single optimal method for all different fiber configurations, suggesting that further studies should be conducted to find the optimal way of combining solutions from different methods. Expand
Fast learning of fiber orientation distribution function for MR tractography using convolutional neural network.
TLDR
A method to reconstruct the fODF from downsampled diffusion-weighted images (DWIs) by leveraging the strong inference ability of the deep convolutional neural network (CNN) and exhibits promising potential in acquisition acceleration for the reconstruction of fODFs with good accuracy. Expand
Using convolution neural networks to learn enhanced fiber orientation distribution models from commercially available diffusion magnetic resonance imaging
TLDR
The use of 3D convolutional neural networks are evaluated to regress multi-shell FOS representations from single-shell representations, using the spherical harmonics basis obtained from constrained spherical deconvolution (CSD) to model FODs. Expand
Estimating fiber orientation distribution from diffusion MRI with spherical needlets
TLDR
It is demonstrated that the proposed method is able to successfully resolve fiber crossings at small angles and automatically identify isotropic diffusion and lead to superior tractography results compared to competing methods. Expand
Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data
TLDR
The aim of this study is to incorporate support for multi-shell data into the CSD approach as well as to exploit the unique b-value dependencies of the different tissue types to estimate a multi-tissue ODF. Expand
Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution
TLDR
The introduction of a constraint on such negative regions is proposed to improve the conditioning of the spherical deconvolution, and this approach is shown to provide FOD estimates that are robust to noise whilst preserving angular resolution. Expand
Quantitative Comparison of Reconstruction Methods for Intra-Voxel Fiber Recovery From Diffusion MRI
TLDR
Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. Expand
Better Fiber ODFs from Suboptimal Data with Autoencoder Based Regularization
TLDR
This work regularizes constrained spherical deconvolution (CSD) with a prior that is derived from an fODF autoencoder, effectively encouraging solutions that are similar to fODFs observed in high-quality training data. Expand
Deep learning reveals untapped information for local white-matter fiber reconstruction in diffusion-weighted MRI.
TLDR
This work highlights the ability of deep learning to capture linkages between ex-vivo ground truth data with feasible MRI sequences and results in intriguingly high reproducibility of orientation structure. Expand
...
1
2
3
...