Compressed Sensing for Rapid MRI: Need for Speed

MRI is a fascinating imaging technology used to visualize the internal structures of the body. However, acquisition speed still remains a challenge especially for patients who are anxious, can’t keep still or have limited breath hold capacity. These challenges can be solved with Compressed Sensing (CS) which helps us in decreasing the acquisition times without sacrificing image quality.

Conventionally, the compression of images is performed after the acquisition of the entire image. This is done to reduce data storage and facilitate transfer of such data. The idea behind CS is to compress and acquire only the most important coefficients of the signal during the acquisition.

3 Requirements for Application of CS

  • Incoherent subsampling for high acquisition speed: MRI involves encoding of spatial frequency information called k-space. To apply CS to MRI, the k-space needs to be randomly undersampled for reducing the acquisition time.
  • Transform sparsity to remove noise from image content: A sparse signal has most of its energy contained in a few measurements while the rest of the measurements are zero or negligible. It is comparatively easy to remove noise from a sparse signal by thresholding. MR images with higher dimensionality (3D or higher) provide better sparsity (similar to image compression) and hence yield better CS performance.
  • Non-linear Iterative reconstruction to balance data inconsistency and sparsity:
    The non-linear reconstruction in CS avoids most of the artifacts that appear in linear
    reconstruction from undersampled data.

Future Potential of CS

  • Rapid 3D Angiography, whole heart coronary imaging and dynamic heart imaging require
    high spatial and temporal resolution. CS improves current strategies by significantly reducing the artifacts that result from undersampling.
  • In brain imaging, the ideas of CS promise to reduce acquisition time while improving the
    resolution of current imagery.
  • CS has also been recently used in clinical applications for pediatric imaging where reduction
    in acquisition time is critical for diagnosis.


  • M. Lustig, D.L Donoho, J.M. Santos, J.M. Pauly, ‘ Compressed Sensing MRI: A look on how CS can improve on current imaging techniques’, IEEE Signal Processing Magazine [72] March 2008
  • M. Lustig, D.L. Donoho and J.M. Pauly, ‘Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging’, Magnetic Resonance in Medicine 58:1182-1195 (2007)
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