# Spherical convolutional neural networks can improve brain microstructure estimation from diffusion MRI data

arXiv: https://arxiv.org/abs/2211.09887 · HTML: https://mlsanity.com/paper/2211.09887/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 59 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications](https://mlsanity.com/paper/1810.12186/) (2018)
- [Equivariant Spherical Deconvolution: Learning Sparse Orientation Distribution Functions from Spherical Data](https://mlsanity.com/paper/2102.09462/) (2021)
- [How can spherical CNNs benefit ML-based diffusion MRI parameter estimation?](https://mlsanity.com/paper/2207.00572/) (2022)

## Built on by (most cited first, 2 of 2)

- [Equivariant Spherical CNNs for Accurate Fiber Orientation Distribution Estimation in Neonatal Diffusion MRI with Reduced Acquisition Time](https://mlsanity.com/paper/2504.01925/) (2025)
- [Protocol generalisation for brain tissue microstructure estimation via hypernetwork-controlled geometric deep learning](https://mlsanity.com/paper/2608.02053/) (2026)

## Abstract (arXiv)

Diffusion magnetic resonance imaging is sensitive to the microstructural properties of brain tissue. However, estimating clinically and scientifically relevant microstructural properties from the measured signals remains a highly challenging inverse problem that machine learning may help solve. This study investigated if recently developed rotationally invariant spherical convolutional neural networks can improve microstructural parameter estimation. We trained a spherical convolutional neural network to predict the ground-truth parameter values from efficiently simulated noisy data and applied the trained network to imaging data acquired in a clinical setting to generate microstructural parameter maps. Our network performed better than the spherical mean technique and multi-layer perceptron, achieving higher prediction accuracy than the spherical mean technique with less rotational variance than the multi-layer perceptron. Although we focused on a constrained two-compartment model of neuronal tissue, the network and training pipeline are generalizable and can be used to estimate the parameters of any Gaussian compartment model. To highlight this, we also trained the network to predict the parameters of a three-compartment model that enables the estimation of apparent neural soma density using tensor-valued diffusion encoding.