# A microstructure estimation Transformer inspired by sparse representation for diffusion MRI

arXiv: https://arxiv.org/abs/2205.06450 · HTML: https://mlsanity.com/paper/2205.06450/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 61 references that are in the map.
- First posted on arXiv 13 May 2022.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Deep MRI Reconstruction: Unrolled Optimization Algorithms Meet Neural Networks](https://mlsanity.com/paper/1907.11711/) (2019)
- [Spherical Harmonic Residual Network for Diffusion Signal Harmonization](https://mlsanity.com/paper/1808.01595/) (2018)
- [Estimation of Tissue Microstructure Using a Deep Network Inspired by a Sparse Reconstruction Framework](https://mlsanity.com/paper/1704.01246/) (2017)
- [Knowledge Transfer between Datasets for Learning-based Tissue Microstructure Estimation](https://mlsanity.com/paper/1910.10930/) (2019)

## Built on by (most cited first, 14 of 14)

- [Diffusion MRI with Machine Learning](https://mlsanity.com/paper/2402.00019/) (2024)
- [Cross-domain Fiber Cluster Shape Analysis for Language Performance Cognitive Score Prediction](https://mlsanity.com/paper/2403.19001/) (2024)
- [ssVERDICT: Self-Supervised VERDICT-MRI for Enhanced Prostate Tumour Characterisation](https://mlsanity.com/paper/2309.06268/) (2023)
- [Reducing Reasoning Costs: The Path of Optimization for Chain of Thought via Sparse Attention Mechanism](https://mlsanity.com/paper/2411.09111/) (2024)
- [Diff-DTI: Fast Diffusion Tensor Imaging Using A Feature-Enhanced Joint Diffusion Model](https://mlsanity.com/paper/2405.15830/) (2024)
- [Simultaneous q-Space Sampling Optimization and Reconstruction for Fast and High-fidelity Diffusion Magnetic Resonance Imaging](https://mlsanity.com/paper/2401.01662/) (2024)
- [AID-DTI: Accelerating High-fidelity Diffusion Tensor Imaging with Detail-Preserving Model-based Deep Learning](https://mlsanity.com/paper/2401.01693/) (2024)
- [DeepMpMRI: Tensor-decomposition Regularized Learning for Fast and High-Fidelity Multi-Parametric Microstructural MR Imaging](https://mlsanity.com/paper/2405.03159/) (2024)
- [SamRobNODDI: Q-Space Sampling-Augmented Continuous Representation Learning for Robust and Generalized NODDI](https://mlsanity.com/paper/2411.06444/) (2024)
- [MRI Parameter Mapping via Gaussian Mixture VAE: Breaking the Assumption of Independent Pixels](https://mlsanity.com/paper/2411.10772/) (2024)
- [AID-DTI: Accelerating High-fidelity Diffusion Tensor Imaging with Detail-preserving Model-based Deep Learning](https://mlsanity.com/paper/2408.10236/) (2024)
- [Ultra-Strong Gradient Diffusion MRI with Self-Supervised Learning for Prostate Cancer Characterization](https://mlsanity.com/paper/2512.03196/) (2025)
- [Diffusion MRI Transformer with a Diffusion Space Rotary Positional Embedding (D-RoPE)](https://mlsanity.com/paper/2603.25977/) (2026)
- [A physics-informed foundation model for quantitative diffusion MRI](https://mlsanity.com/paper/2606.00156/) (2026)

## Abstract (arXiv)

Diffusion magnetic resonance imaging (dMRI) is an important tool in characterizing tissue microstructure based on biophysical models, which are complex and highly non-linear. Resolving microstructures with optimization techniques is prone to estimation errors and requires dense sampling in the q-space. Deep learning based approaches have been proposed to overcome these limitations. Motivated by the superior performance of the Transformer, in this work, we present a learning-based framework based on Transformer, namely, a Microstructure Estimation Transformer with Sparse Coding (METSC) for dMRI-based microstructure estimation with downsampled q-space data. To take advantage of the Transformer while addressing its limitation in large training data requirements, we explicitly introduce an inductive bias - model bias into the Transformer using a sparse coding technique to facilitate the training process. Thus, the METSC is composed with three stages, an embedding stage, a sparse representation stage, and a mapping stage. The embedding stage is a Transformer-based structure that encodes the signal to ensure the voxel is represented effectively. In the sparse representation stage, a dictionary is constructed by solving a sparse reconstruction problem that unfolds the Iterative Hard Thresholding (IHT) process. The mapping stage is essentially a decoder that computes the microstructural parameters from the output of the second stage, based on the weighted sum of normalized dictionary coefficients where the weights are also learned. We tested our framework on two dMRI models with downsampled q-space data, including the intravoxel incoherent motion (IVIM) model and the neurite orientation dispersion and density imaging (NODDI) model. The proposed method achieved up to 11.25 folds of acceleration in scan time and outperformed the other state-of-the-art learning-based methods.