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A convergence analysis for projected fast iterative soft-thresholding algorithm under radial sampling MRI.

Biao Qu1, Zuwen Zhang2, Yewei Chen2

  • 1Department of Instrumental and Electrical Engineering, Xiamen University, Xiamen, China.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|April 15, 2023
PubMed
Summary
This summary is machine-generated.

This study establishes convergence conditions for the projected fast iterative soft-thresholding algorithm (pFISTA) in radial magnetic resonance imaging (MRI). Optimized parameters ensure fast and clear image reconstruction from undersampled data.

Keywords:
Compressed sensingFast algorithmImage reconstructionMRIRadial sampling

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Area of Science:

  • Medical Imaging
  • Magnetic Resonance Imaging (MRI)
  • Image Reconstruction

Background:

  • Radial sampling accelerates MRI acquisition but undersampling introduces artifacts.
  • Tight-frame sparse reconstruction models effectively reduce these artifacts.
  • The convergence of the projected fast iterative soft-thresholding algorithm (pFISTA) for radial sampling requires theoretical clarification.

Purpose of the Study:

  • To derive a theoretical convergence condition for pFISTA in radial MRI.
  • To optimize the algorithm's performance for faster image reconstruction.
  • To validate the findings on in vivo MRI data.

Main Methods:

  • Derived a theoretical convergence condition for pFISTA under radial sampling.
  • Estimated the maximal eigenvalue of reconstruction operators using power iteration.
  • Determined an optimal step size for accelerated convergence.

Main Results:

  • Established a theoretical convergence condition for pFISTA in radial MRI.
  • Identified an optimal step size for the algorithm.
  • Demonstrated fast convergence with the recommended parameter on in vivo static brain and dynamic contrast-enhanced liver imaging data.

Conclusions:

  • The derived convergence condition and suggested optimal step size enhance pFISTA performance for radial MRI.
  • This approach facilitates faster and clearer image reconstruction from undersampled radial MRI data.
  • The findings are validated for both static and dynamic in vivo imaging applications.