The DOI matches its Crossref record; 43 of the 43 references it cites were found in a registry or an index.
Diffusion MRI noise mapping using random matrix theory
Open accessAbstract
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
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
LIII. On lines and planes of closest fit to systems of points in space
Pearson, K. (1901) · The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786440109462720 · Cited by 11,934
Analysis of a complex of statistical variables into principal components.
Hotelling, H. (1933) · Journal of Educational Psychology · doi:10.1037/h0071325 · Cited by 9,633
Generalized autocalibrating partially parallel acquisitions (GRAPPA)
Griswold, M. A., Jakob, P. M., Heidemann, R. M., Nittka, M., Jellus, V., Wang, J., Kiefer, B., & Haase, A. (2002) · Magnetic Resonance in Medicine · doi:10.1002/mrm.10171 · Cited by 5,303
Statistical Theory of the Energy Levels of Complex Systems. I
Dyson, F. J. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1703773 · Cited by 2,266
Lower Limit for the Energy Derivative of the Scattering Phase Shift
Wigner, E. P. (1955) · Physical Review · doi:10.1103/physrev.98.145 · Cited by 2,010
DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
Marčenko, V. A., & Pastur, L. A. (1967) · Mathematics of the USSR-Sbornik · doi:10.1070/sm1967v001n04abeh001994 · Cited by 1,713
Methods for Solving Incorrectly Posed Problems
Morozov, V. A. (1984) · Springer eBooks · doi:10.1007/978-1-4612-5280-1 · Cited by 1,357
Noise Dressing of Financial Correlation Matrices
Laloux, L., Cizeau, P., Bouchaud, J.-P., & Potters, M. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.1467 · Cited by 1,241
Dietrich, O., Raya, J. G., Reeder, S. B., Reiser, M. F., & Schoenberg, S. O. (2007) · Journal of Magnetic Resonance Imaging · doi:10.1002/jmri.20969 · Cited by 992
Diffusion tensor imaging and beyond
Tournier, J., Mori, S., & Leemans, A. (2011) · Magnetic Resonance in Medicine · doi:10.1002/mrm.22924 · Cited by 921
Cited by
Denoising of diffusion MRI using random matrix theory
Veraart, J., Novikov, D. S., Christiaens, D., Ades-aron, B., Sijbers, J., & Fieremans, E. (2016) · NeuroImage · doi:10.1016/j.neuroimage.2016.08.016 · Cited by 1,905
Self-citationQuantifying brain microstructure with diffusion MRI: Theory and parameter estimation
Novikov, D. S., Fieremans, E., Jespersen, S. N., & Kiselev, V. G. (2019) · NMR in Biomedicine · doi:10.1002/nbm.3998 · Cited by 581
Self-citationDegeneracy in model parameter estimation for multi‐compartmental diffusion in neuronal tissue
Jelescu, I. O., Veraart, J., Fieremans, E., & Novikov, D. S. (2016) · NMR in Biomedicine · doi:10.1002/nbm.3450 · Cited by 316
Self-citationFibre-specific white matter reductions in Alzheimer’s disease and mild cognitive impairment
Mito, R., Raffelt, D., Dhollander, T., Vaughan, D. N., Tournier, J.-D., Salvado, O., Brodtmann, A., Rowe, C. C., Villemagne, V. L., & Connelly, A. (2018) · Brain · doi:10.1093/brain/awx355 · Cited by 309
TE dependent Diffusion Imaging (TEdDI) distinguishes between compartmental T2 relaxation times
Veraart, J., Novikov, D. S., & Fieremans, E. (2018) · NeuroImage · doi:10.1016/j.neuroimage.2017.09.030 · Cited by 212
Self-citation
Metadata
- Authors
- Veraart, J., Fieremans, E., & Novikov, D. S.
- Venue
- Magnetic Resonance in Medicine
- Publisher
- Wiley
- Published
- 2015-11-24
- Volume
- 76
- Issue
- 5
- Pages
- 1582-1593
- ISSN
- 0740-3194 (ISSN-L)
- 1522-2594
- OpenAlex
- W2177917702
- Cited by
- 773
- References
- 43
- FWCI
- 16.46
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Diffusion MRI noise mapping using random matrix theory. https://app.cochat.ai/papers/10.1002/mrm.26059
- The paper
- Veraart, J., Fieremans, E., & Novikov, D. S. (2016). Diffusion MRI noise mapping using random matrix theory. Magnetic Resonance in Medicine. https://doi.org/10.1002/mrm.26059
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
