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Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging (2007)
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| Venue: | MAGNETIC RESONANCE IN MEDICINE 58:1182–1195 |
| Citations: | 535 - 11 self |
BibTeX
@MISC{Lustig07sparsemri:,
author = {Michael Lustig and David Donoho and John M. Pauly},
title = {Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging},
year = {2007}
}
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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 compressedsensing, 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 ℓ1 norm of a transformed image, subject to data fidelity constraints. Examples demonstrate improved spatial resolution and accelerated acquisition for multislice fast spinecho brain imaging and 3D contrast enhanced angiography.
Keyphrases
compressed sensing magnetic resonance rapid mr imaging mr image sparse representation significant coefficient appropriate nonlinear recovery scheme transformed image undersample k-space pseudo-random variable-density undersampling undersampling add practical incoherent k-space data sparse coefficient pixel representation complicated image noise-like interference mathematical theory transform domain spatial finite-differences spinecho brain imaging data fidelity constraint accelerated acquisition sparse transform spatial resolution wavelet coefficient aliasing interference
