# Complex diffusion-weighted image estimation via matrix recovery under general noise models

arXiv: https://arxiv.org/abs/1812.05954 · HTML: https://mlsanity.com/paper/1812.05954/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2018.

## Built on by (most cited first, 8 of 8)

- [Self-Supervised Diffusion MRI Denoising via Iterative and Stable Refinement](https://mlsanity.com/paper/2501.13514/) (2025)
- [Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methods](https://mlsanity.com/paper/2405.13912/) (2024)
- [HAITCH: A Framework for Distortion and Motion Correction in Fetal Multi-Shell Diffusion-Weighted MRI](https://mlsanity.com/paper/2406.20042/) (2024)
- [Diff5T: Benchmarking Human Brain Diffusion MRI with an Extensive 5.0 Tesla K-Space and Spatial Dataset](https://mlsanity.com/paper/2412.06666/) (2024)
- [μGUIDE: a framework for quantitative imaging via generalized uncertainty-driven inference using deep learning](https://mlsanity.com/paper/2312.17293/) (2023)
- [MBD: Multi b-value Denoising of Diffusion Magnetic Resonance Images](https://mlsanity.com/paper/2410.16898/) (2024)
- [Ultra-Strong Gradient Diffusion MRI with Self-Supervised Learning for Prostate Cancer Characterization](https://mlsanity.com/paper/2512.03196/) (2025)
- [A Stationarity-and-Coupling Criterion for Training-Free Time-Lagged Spectral Embeddings of Multivariate Time Series](https://mlsanity.com/paper/2606.13823/) (2026)

## Abstract (arXiv)

We propose a patch-based singular value shrinkage method for diffusion magnetic resonance image estimation targeted at low signal to noise ratio and accelerated acquisitions. It operates on the complex data resulting from a sensitivity encoding reconstruction, where asymptotically optimal signal recovery guarantees can be attained by modeling the noise propagation in the reconstruction and subsequently simulating or calculating the limit singular value spectrum. Simple strategies are presented to deal with phase inconsistencies and optimize patch construction. The pertinence of our contributions is quantitatively validated on synthetic data, an in vivo adult example, and challenging neonatal and fetal cohorts. Our methodology is compared with related approaches, which generally operate on magnitude-only data and use data-based noise level estimation and singular value truncation. Visual examples are provided to illustrate effectiveness in generating denoised and debiased diffusion estimates with well preserved spatial and diffusion detail.