Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization

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340 Scopus citations


In clinical magnetic resonance imaging (MRI), any reduction in scan time offers a number of potential benefits ranging from high-temporal-rate observation of physiological processes to improvements in patient comfort. Following recent developments in compressive sensing (CS) theory, several authors have demonstrated that certain classes of MR images which possess sparse representations in some transform domain can be accurately reconstructed from very highly undersampled K-space data by solving a convex l0 -minimization problem. Although l1-based techniques are extremely powerful, they inherently require a degree of over-sampling above the theoretical minimum sampling rate to guarantee that exact reconstruction can be achieved. In this paper, we propose a generalization of the CS paradigm based on homotopic approximation of the l0 quasi-norm and show how MR image reconstruction can be pushed even further below the Nyquist limit and significantly closer to the theoretical bound. Following a brief review of standard CS methods and the developed theoretical extensions, several example MRI reconstructions from highly undersampled K-space data are presented.

Original languageEnglish (US)
Article number4556634
Pages (from-to)106-121
Number of pages16
JournalIEEE transactions on medical imaging
Issue number1
StatePublished - Jan 2009


  • Compressed sensing
  • Compressive sensing (CS)
  • Image reconstruction
  • Magnetic resonance imaging (MRI)
  • Nonconvex optimization

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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