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Cited by 6,952Advanced MRI Techniques and ApplicationsSparse and Compressive Sensing TechniquesImage and Signal Denoising Methods

Sparse MRI: The application of compressed sensing for rapid MR imaging

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Lustig, Michael, Donoho, David, Pauly, John M.·2007·Magnetic Resonance in Medicine
DOI 10.1002/mrm.21391
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Abstract

The sparsity which is implicit in MR images is exploited to significantly undersample k ‐space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finite‐differences or their wavelet coefficients. According to the recently developed mathematical theory of compressed‐sensing, images with a sparse representation can be recovered from randomly undersampled k ‐space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise‐like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo‐random variable‐density undersampling of phase‐encodes. The reconstruction is performed by minimizing the ℓ 1 norm of a transformed image, subject to data fidelity constraints. Examples demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin‐echo brain imaging and 3D contrast enhanced angiography. Magn Reson Med, 2007. © 2007 Wiley‐Liss, Inc.

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  • Compressed sensing is an accelerated imaging method that enables reconstruction of undersampled data by exploiting image sparsity.

    “Compressed sensing (CS) is an accelerated imaging method, which enables reconstruction of under sampled data by exploiting image sparsity (Wang et al. 2018b; Lustig et al. 2007).”

    From Neurite orientation dispersion and density imaging of mouse brain microstructure (2019) · cites this paper as Lustig et al. 2007

  • Undersampling both phase encoding directions helps to fully explore the 2D sparsity preferred in CS reconstruction.

    “Undersampling both phase encoding directions helps to fully explore the 2D sparsity preferred in CS reconstruction (Lustig et al. 2007; Wang et al. 2019).”

    From Neurite orientation dispersion and density imaging of mouse brain microstructure (2019) · cites this paper as Lustig et al. 2007

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Research works printed but not linked: 39

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Authors
Lustig, M., Donoho, D., & Pauly, J. M.
Affiliations
Stanford University (US)
Corresponding author
Lustig, Michael
ORCID
Venue
Magnetic Resonance in Medicine
Publisher
Wiley
Published
2007-10-29
Volume
58
Issue
6
Pages
1182-1195
ISSN
  • 0740-3194 (ISSN-L)
  • 1522-2594
DOI
10.1002/mrm.21391
OpenAlex
W2101675075
Cited by
6,952
References
0
Citations by year
2026: 277 · 2025: 391 · 2024: 410 · 2023: 432 · 2022: 411 · 2021: 531 · 2020: 501 · 2019: 509 · 2018: 417 · 2017: 406 · 2016: 415 · 2015: 419 · 2014: 413 · 2013: 381 · 2012: 346
FWCI
104.09
Type
journal article
Language
en
Open access
Licence
onlinelibrary.wiley.com/termsAndConditions#vor (vor)
Locations
  • Magnetic Resonance in Medicine (publishedVersion)
  • PubMed (publishedVersion)
Funders
  • National Science Foundation (0505303)
  • National Institutes of Health (5r01hl074332-04)
  • National Heart, Lung, and Blood Institute (R01-HL074332, R01HL067161, R01HL075803)
Topics
  • Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
  • Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
Keywords
compressed sensing, k-space undersampling, nonlinear thresholding, l1-norm minimization, contrast-enhanced angiography
MeSH terms
Algorithms, Artificial Intelligence, Brain, Humans, Image Enhancement, Image Interpretation, Computer-Assisted, Magnetic Resonance Imaging, Pattern Recognition, Automated, Sensitivity and Specificity, Reproducibility of Results, Phantoms, Imaging, Imaging, Three-Dimensional, Data Compression

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