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# Diffusion MRI noise mapping using random matrix theory.

### Author information

- 1
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA. Jelle.veraart@nyumc.org.
- 2
- Department of Physics, iMinds-Vision Lab, University of Antwerp, Antwerp, Belgium. Jelle.veraart@nyumc.org.
- 3
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA.

### Abstract

#### PURPOSE:

To estimate the spatially varying noise map using a redundant series of magnitude MR images.

#### METHODS:

We exploit redundancy in non-Gaussian distributed multidirectional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices. The bulk of principal component analysis eigenvalues, arising due to noise, is described by the universal Marchenko-Pastur distribution, parameterized by the noise level. This allows us to estimate noise level in a local neighborhood based on the singular value decomposition of a matrix combining neighborhood voxels and diffusion directions.

#### RESULTS:

We present a model-independent local noise mapping method capable of estimating the noise level down to about 1% error. In contrast to current state-of-the-art techniques, the resultant noise maps do not show artifactual anatomical features that often reflect physiological noise, the presence of sharp edges, or a lack of adequate a priori knowledge of the expected form of MR signal.

#### CONCLUSIONS:

Simulations and experiments show that typical diffusion MRI data exhibit sufficient redundancy that enables accurate, precise, and robust estimation of the local noise level by interpreting the principal component analysis eigenspectrum in terms of the Marchenko-Pastur distribution. Magn Reson Med 76:1582-1593, 2016. © 2015 International Society for Magnetic Resonance in Medicine.

© 2015 International Society for Magnetic Resonance in Medicine.

#### KEYWORDS:

Marchenko-Pastur; Rician; diffusion MRI; noise; principal component analysis

- PMID:
- 26599599
- PMCID:
- PMC4879661
- DOI:
- 10.1002/mrm.26059

- [Indexed for MEDLINE]

### Publication types, MeSH terms, Grant support

#### Publication types

#### MeSH terms

- Algorithms*
- Brain/anatomy & histology
- Computer Simulation
- Data Interpretation, Statistical*
- Diffusion Magnetic Resonance Imaging/methods*
- Humans
- Image Interpretation, Computer-Assisted/methods*
- Models, Statistical*
- Principal Component Analysis
- Reproducibility of Results
- Sensitivity and Specificity
- Signal-To-Noise Ratio*