Accelerating Non-Cartesian MRI Reconstruction Convergence Using k-Space Preconditioning

Frank Ong, Martin Uecker, Michael Lustig

Research output: Contribution to journalArticlepeer-review


We propose a k-space preconditioning formulation for accelerating the convergence of iterative Magnetic Resonance Imaging (MRI) reconstructions from non-uniformly sampled k-space data. Existing methods either use sampling density compensations which sacrifice reconstruction accuracy, or circulant preconditioners which increase per-iteration computation. Our approach overcomes both shortcomings. Concretely, we show that viewing the reconstruction problem in the dual formulation allows us to precondition in k-space using density-compensation-like operations. Using the primal-dual hybrid gradient method, the proposed preconditioning method does not have inner loops and are competitive in accelerating convergence compared to existing algorithms. We derive ℓ2-optimized preconditioners, and demonstrate through experiments that the proposed method converges in about ten iterations in practice.
Original languageEnglish
Pages (from-to)1646-1654
JournalIEEE Transactions on Medical Imaging
Issue number5
Publication statusPublished - May 2020
Externally publishedYes


  • Image reconstruction
  • Convergence
  • Magnetic resonance imaging
  • Gradient methods
  • Acceleration
  • Trajectory
  • MRI
  • iterative reconstruction
  • non-cartesian
  • preconditioner
  • density compensation

Fields of Expertise

  • Human- & Biotechnology
  • Information, Communication & Computing


Dive into the research topics of 'Accelerating Non-Cartesian MRI Reconstruction Convergence Using k-Space Preconditioning'. Together they form a unique fingerprint.

Cite this