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Monotone FISTA with Variable Acceleration for Compressed Sensing Magnetic Resonance Imaging.

Marcelo V W Zibetti1, Elias S Helou2, Ravinder R Regatte1

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Summary
This summary is machine-generated.

A new modification to the monotone fast iterative shrinkage-thresholding algorithm (MFISTA) accelerates convergence for compressed sensing in magnetic resonance imaging. This enhanced MFISTA offers improved theoretical bounds and parameter flexibility.

Keywords:
FISTAcompressed sensingiterative algorithmsmagnetic resonance imagingproximal-gradient methods

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Area of Science:

  • Applied Mathematics
  • Medical Imaging
  • Optimization Algorithms

Background:

  • Compressed sensing (CS) is crucial for accelerating magnetic resonance imaging (MRI) acquisition.
  • Existing algorithms like monotone fast iterative shrinkage-thresholding algorithm (MFISTA) face limitations in reconstruction time.
  • The need for faster convergence in iterative algorithms for MRI reconstruction is significant.

Purpose of the Study:

  • To enhance the convergence speed of the MFISTA algorithm for compressed sensing MRI.
  • To reduce the overall reconstruction time in MRI scans.
  • To extend FISTA-like methods to complex variables for broader applicability.

Main Methods:

  • Introduced an extra term, a multiple of the proximal-gradient step, into the MFISTA momentum formula.
  • Modified the algorithm to select the next iterate from improved points using methods like arbitrary shifts or line searches.
  • Provided a careful extension of FISTA-like methods to functions of several complex variables.

Main Results:

  • The modified MFISTA algorithm demonstrates accelerated convergence compared to the original MFISTA.
  • Improved theoretical convergence bounds were established for the enhanced algorithm.
  • The modified algorithm offers greater flexibility in parameter selection.

Conclusions:

  • The proposed MFISTA modification effectively reduces reconstruction time in compressed sensing MRI.
  • The enhanced algorithm provides superior convergence properties and flexibility.
  • The extension to complex variables broadens the potential applications of these methods.