High-dimensional MR imaging often requires long data acquisition time, thereby limiting its practical applications. This paper presents a low-rank tensor based method for accelerated high-dimensional MR imaging using sparse sampling. This method represents high-dimensional images as low-rank tensors (or partially separable functions) and uses this mathematical structure for sparse sampling of the data space and for image reconstruction from highly undersampled data. More specifically, the proposed method acquires two datasets with complementary sampling patterns, one for subspace estimation and the other for image reconstruction; image reconstruction from highly undersampled data is accomplished by fitting the measured data with a sparsity constraint on the core tensor and a group sparsity constraint on the spatial coefficients jointly using the alternating direction method of multipliers. The usefulness of the proposed method is demonstrated in MRI applications; it may also have applications beyond MRI.

Original languageEnglish (US)
Article number7451247
Pages (from-to)2119-2129
Number of pages11
JournalIEEE transactions on medical imaging
Issue number9
StatePublished - Sep 2016


  • High-dimensional MR imaging
  • low-rank tensor
  • partial separability
  • sparse regularization
  • sparse sampling

ASJC Scopus subject areas

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


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