SIGNAL (programming language)

Quantum mechanics

Truncation (statistics)

Algorithm

Engineering

Eigenvalues and eigenvectors

Computer science

Mathematical optimization

Thermodynamics

Physics

Singular value decomposition

Diffusion

Mathematics

Image (mathematics)

Synthetic data

Electronic engineering

Artificial intelligence

Sensitivity (control systems)

Programming language

Noise (video)

Singular value

Machine learning

NeuroImage

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.

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