Accelerating dynamic spiral MRI by algebraic reconstruction from undersampled k-t space

Taehoon Shin, Jon Fredrik Nielsen, Krishna S. Nayak

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The temporal resolution of dynamic magnetic resonance imaging (MRI) can be increased by sampling a fraction of k-space in an interleaved fashion, which introduces spatial and temporal aliasing. We describe algebraically and graphically the aliasing process caused by dynamic undersampled spiral imaging within 3-D xy f space (the Fourier transform of k xk yt space) and formulate the unaliasing problem as a set of independent linear inversions. Since each linear system is numerically underdetermined, the use of prior knowledge in the form of bounded support regions is proposed. To overcome the excessive memory requirements for handling large matrices, a fast implementation of the conjugate gradient (CG) method is used. Numerical simulation and in vivo experiments using spiral twofold undersampling demonstrate reduced motion artifacts and the improved depiction of fine cardiac structures. The achieved reduction of motion artifacts and motion blur is comparable to simple filtering, which is computationally more efficient, while the proposed algebraic framework offers greater flexibility to incorporate additional algebraic acceleration techniques and to handle arbitrary sampling schemes.

Original languageEnglish
Pages (from-to)917-924
Number of pages8
JournalIEEE Transactions on Medical Imaging
Issue number7
StatePublished - Jul 2007

Bibliographical note

Funding Information:
Manuscript received January 14, 2007; revised February 15, 2007. This work was supported in part by American Heart Association under Grant 0435249N, in part by the National Institutes of Health under Grant R01-HL074332, in part by the James Zumberge Foundation, and in part by GE Healthcare. Asterisk indicates corresponding author. *T. Shin is with the University of Southern California, Los Angeles, CA 90089 USA (e-mail: J.-F. Nielsen and K. S. Nayak are with the University of Southern California, Los Angeles, CA 90089 USA. Digital Object Identifier 10.1109/TMI.2007.895450


  • Algebraic reconstruction
  • Dynamic imaging
  • Fast imaging
  • Spiral cardiac magnetic resonance imaging (MRI)
  • Temporal acceleration


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