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

      1 , ,
      Magnetic resonance in medicine
      Wiley

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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.

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          Author and article information

          Journal
          Magn Reson Med
          Magnetic resonance in medicine
          Wiley
          0740-3194
          0740-3194
          Dec 2007
          : 58
          : 6
          Affiliations
          [1 ] Magnetic Resonance Systems Research Laboratory, Department of Electrical Engineering, Stanford University, Stanford, California 94305-9510, USA. mlustig@mrsrl.stanford.edu
          Article
          10.1002/mrm.21391
          17969013
          89fb5c9e-29e4-4035-8f66-5dbec0e4b322
          (c) 2007 Wiley-Liss, Inc.
          History

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