# Neural Spherical Harmonics for structurally coherent continuous representation of diffusion MRI signal

arXiv: https://arxiv.org/abs/2308.08210 · HTML: https://mlsanity.com/paper/2308.08210/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 20 references that are in the map.
- First posted on arXiv 16 Aug 2023.

## Builds on (most cited first, 5 of 5)

- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Lossy compression of multidimensional medical images using sinusoidal activation networks: an evaluation study](https://mlsanity.com/paper/2208.01602/) (2022)

## Built on by (most cited first, 5 of 5)

- [Estimating Neural Orientation Distribution Fields on High Resolution Diffusion MRI Scans](https://mlsanity.com/paper/2409.09387/) (2024)
- [Implicit neural representations for accurate estimation of the standard model of white matter](https://mlsanity.com/paper/2506.15762/) (2025)
- [MICCAI-CDMRI 2023 QuantConn Challenge Findings on Achieving Robust Quantitative Connectivity through Harmonized Preprocessing of Diffusion MRI](https://mlsanity.com/paper/2411.09618/) (2024)
- [SIINR: Structurally Informed Implicit Neural Representations for super-resolution with uncertainty quantification of clinical quality diffusion MRI datasets](https://mlsanity.com/paper/2607.19943/) (2026)
- [Diffusion-Encoding Gaussian Field for Joint k-q dMRI Reconstruction](https://mlsanity.com/paper/2609.02288/) (2026)

## Abstract (arXiv)

We present a novel way to model diffusion magnetic resonance imaging (dMRI) datasets, that benefits from the structural coherence of the human brain while only using data from a single subject. Current methods model the dMRI signal in individual voxels, disregarding the intervoxel coherence that is present. We use a neural network to parameterize a spherical harmonics series (NeSH) to represent the dMRI signal of a single subject from the Human Connectome Project dataset, continuous in both the angular and spatial domain. The reconstructed dMRI signal using this method shows a more structurally coherent representation of the data. Noise in gradient images is removed and the fiber orientation distribution functions show a smooth change in direction along a fiber tract. We showcase how the reconstruction can be used to calculate mean diffusivity, fractional anisotropy, and total apparent fiber density. These results can be achieved with a single model architecture, tuning only one hyperparameter. In this paper we also demonstrate how upsampling in both the angular and spatial domain yields reconstructions that are on par or better than existing methods.