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

## TL;DR

This paper introduces a novel patch-based singular value shrinkage method for complex diffusion MRI data, improving denoising and estimation accuracy under low SNR and accelerated acquisition conditions.

## Contribution

It presents a new complex data processing approach with optimal noise modeling and singular value spectrum analysis, enhancing diffusion MRI estimation over magnitude-only methods.

## Key findings

- Effective denoising and debiasing demonstrated on synthetic and real data
- Outperforms magnitude-only approaches in preserving spatial and diffusion details
- Validated on challenging neonatal and fetal MRI datasets

## Abstract

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.