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Related Experiment Video

Updated: Feb 6, 2026

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Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for

Kirsten Koolstra1, Jeroen van Gemert2, Peter Börnert1,3

  • 1C. J. Gorter Center for High Field MRI, Department of Radiology, Leiden University Medical Center, Leiden, The Netherlands.

Magnetic Resonance in Medicine
|August 8, 2018
PubMed
Summary
This summary is machine-generated.

A new preconditioner speeds up parallel imaging (PI) and compressed sensing (CS) MRI reconstructions. This method significantly reduces computation time without affecting image quality, making large-scale reconstructions more efficient.

Keywords:
compressed sensingparallel imagingpreconditioningsplit bregman

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Area of Science:

  • Medical Imaging
  • Computational Science

Background:

  • Parallel Imaging (PI) and Compressed Sensing (CS) MRI reconstructions are computationally intensive.
  • Large linear systems in PI and CS algorithms require significant processing time, especially with increasing problem size or coil numbers.
  • Effective preconditioning techniques are crucial for accelerating these linear system solutions.

Purpose of the Study:

  • To design a preconditioner for accelerating parallel imaging (PI) and compressed sensing (CS) MRI reconstructions using Cartesian trajectories.
  • To develop a fast and efficient method for solving large linear systems inherent in PI and CS algorithms.

Main Methods:

  • Approximated the system matrix of the linear system with a block circulant matrix with circulant blocks.
  • Utilized the fast Fourier transform (FFT) for rapid preconditioner construction and inverse evaluation.
  • Integrated the preconditioner with the conjugate gradient method within the Split Bregman algorithm for MRI reconstruction.

Main Results:

  • The designed circulant preconditioner reduced conjugate gradient iterations by nearly a factor of 5.
  • Achieved a total acceleration factor of approximately 2.5 for the entire reconstruction algorithm in MATLAB.
  • Demonstrated negligible initialization time for the preconditioner.

Conclusions:

  • The proposed preconditioner effectively reduces MRI reconstruction time for PI and CS using Split Bregman.
  • Maintains reconstruction stability while handling large systems due to its Fourier-based nature.
  • Enables efficient computations for large-scale imaging problems.