# Implicit neural representations for accurate estimation of the standard model of white matter

arXiv: https://arxiv.org/abs/2506.15762 · HTML: https://mlsanity.com/paper/2506.15762/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 84 references that are in the map.
- First posted on arXiv 18 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Learned Initializations for Optimizing Coordinate-Based Neural Representations](https://mlsanity.com/paper/2012.02189/) (2020)
- [Gibbs-Ringing Artifact Removal Based on Local Subvoxel-shifts](https://mlsanity.com/paper/1501.07758/) (2015)
- [Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI](https://mlsanity.com/paper/1609.09144/) (2016)
- [SCARF: Scalable Continual Learning Framework for Memory-efficient Multiple Neural Radiance Fields](https://mlsanity.com/paper/2409.04482/) (2024)
- [Neural Orientation Distribution Fields for Estimation and Uncertainty Quantification in Diffusion MRI](https://mlsanity.com/paper/2307.08138/) (2023)
- [Neural Spherical Harmonics for structurally coherent continuous representation of diffusion MRI signal](https://mlsanity.com/paper/2308.08210/) (2023)
- [Learning Spatially-Continuous Fiber Orientation Functions](https://mlsanity.com/paper/2312.05721/) (2023)
- [Rician likelihood loss for quantitative MRI using self-supervised deep learning](https://mlsanity.com/paper/2307.07072/) (2023)
- [ssVERDICT: Self-Supervised VERDICT-MRI for Enhanced Prostate Tumour Characterisation](https://mlsanity.com/paper/2309.06268/) (2023)
- [Estimating Neural Orientation Distribution Fields on High Resolution Diffusion MRI Scans](https://mlsanity.com/paper/2409.09387/) (2024)
- [Parameter estimation for WMTI-Watson model of white matter using encoder-decoder recurrent neural network](https://mlsanity.com/paper/2203.00595/) (2022)
- [Fitting a Directional Microstructure Model to Diffusion-Relaxation MRI Data with Self-Supervised Machine Learning](https://mlsanity.com/paper/2210.02349/) (2022)

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

- [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)
- [Ultra-Strong Gradient Diffusion MRI with Self-Supervised Learning for Prostate Cancer Characterization](https://mlsanity.com/paper/2512.03196/) (2025)

## Abstract (arXiv)

Diffusion magnetic resonance imaging (dMRI) enables non-invasive investigation of tissue microstructure. The Standard Model (SM) of white matter aims to disentangle dMRI signal contributions from intra- and extra-axonal water compartments. However, due to the model its high-dimensional nature, accurately estimating its parameters poses a complex problem and remains an active field of research, in which different (machine learning) strategies have been proposed. This work introduces an estimation framework based on implicit neural representations (INRs), which incorporate spatial regularization through the sinusoidal encoding of the input coordinates. The INR method is evaluated on both synthetic and in vivo datasets and compared to existing methods. Results demonstrate superior accuracy of the INR method in estimating SM parameters, particularly in low signal-to-noise conditions. Additionally, spatial upsampling of the INR can represent the underlying dataset anatomically plausibly in a continuous way. The INR is self-supervised, eliminating the need for labeled training data. It achieves fast inference, is robust to noise, supports joint estimation of SM kernel parameters and the fiber orientation distribution function with spherical harmonics orders up to at least 8, and accommodates gradient non-uniformity corrections. The combination of these properties positions INRs as a potentially important tool for analyzing and interpreting diffusion MRI data.