# Recovering high-quality FODs from a reduced number of diffusion-weighted images using a model-driven deep learning architecture

arXiv: https://arxiv.org/abs/2307.15273 · HTML: https://mlsanity.com/paper/2307.15273/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 28 Jul 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1703.00555/) (2017)
- [TractSeg - Fast and accurate white matter tract segmentation](https://mlsanity.com/paper/1805.07103/) (2018)
- [VS-Net: Variable splitting network for accelerated parallel MRI reconstruction](https://mlsanity.com/paper/1907.10033/) (2019)
- [Learning a Model-Driven Variational Network for Deformable Image Registration](https://mlsanity.com/paper/2105.12227/) (2021)
- [Equivariant Spherical Deconvolution: Learning Sparse Orientation Distribution Functions from Spherical Data](https://mlsanity.com/paper/2102.09462/) (2021)
- [Deep Learning Estimation of Multi-Tissue Constrained Spherical Deconvolution with Limited Single Shell DW-MRI](https://mlsanity.com/paper/2002.08820/) (2020)
- [A machine learning-based method for estimating the number and orientations of major fascicles in diffusion-weighted magnetic resonance imaging](https://mlsanity.com/paper/2006.11117/) (2020)

## Built on by (most cited first, 3 of 3)

- [FOD-Swin-Net: angular super resolution of fiber orientation distribution using a transformer-based deep model](https://mlsanity.com/paper/2402.11775/) (2024)
- [From Promise to Practical Reality: Transforming Diffusion MRI Analysis with Fast Deep Learning Enhancement](https://mlsanity.com/paper/2508.10950/) (2025)
- [FOD-Diff: 3D Multi-Channel Patch Diffusion Model for Fiber Orientation Distribution](https://mlsanity.com/paper/2512.16075/) (2025)

## Abstract (arXiv)

Fibre orientation distribution (FOD) reconstruction using deep learning has the potential to produce accurate FODs from a reduced number of diffusion-weighted images (DWIs), decreasing total imaging time. Diffusion acquisition invariant representations of the DWI signals are typically used as input to these methods to ensure that they can be applied flexibly to data with different b-vectors and b-values; however, this means the network cannot condition its output directly on the DWI signal. In this work, we propose a spherical deconvolution network, a model-driven deep learning FOD reconstruction architecture, that ensures intermediate and output FODs produced by the network are consistent with the input DWI signals. Furthermore, we implement a fixel classification penalty within our loss function, encouraging the network to produce FODs that can subsequently be segmented into the correct number of fixels and improve downstream fixel-based analysis. Our results show that the model-based deep learning architecture achieves competitive performance compared to a state-of-the-art FOD super-resolution network, FOD-Net. Moreover, we show that the fixel classification penalty can be tuned to offer improved performance with respect to metrics that rely on accurately segmented of FODs. Our code is publicly available at https://github.com/Jbartlett6/SDNet .