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A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI.

Tao Hong1, Luis Hernandez-Garcia1, Jeffrey A Fessler2

  • 1Department of Radiology, University of Michigan, Ann Arbor, MI 48109, USA.

IEEE Transactions on Computational Imaging
|October 10, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a new complex quasi-Newton proximal method (CQNPM) for faster compressed sensing (CS) MRI reconstruction. Efficiently solving weighted proximal mappings (WPM) makes CQNPM practical for reconstructing non-Cartesian MRI data.

Keywords:
Compressed sensingmagnetic resonance imaging (MRI)non-Cartesian trajectorysecond-ordersparsitytotal variationwavelets

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Area of Science:

  • Medical Imaging
  • Optimization Algorithms
  • Signal Processing

Background:

  • Model-based methods are crucial for compressed sensing (CS) magnetic resonance imaging (MRI) reconstruction.
  • These methods rely on regularizers to characterize image properties.
  • Reconstruction is typically framed as a composite optimization problem, often tackled by accelerated proximal methods (APMs).

Purpose of the Study:

  • To propose a novel complex quasi-Newton proximal method (CQNPM) for CS MRI reconstruction.
  • To address the computational challenge of weighted proximal mappings (WPM) within CQNPM.
  • To enhance the efficiency and practicality of advanced reconstruction techniques in MRI.

Main Methods:

  • Development of a complex quasi-Newton proximal method (CQNPM).
  • Integration of wavelet and total variation regularizers for CS MRI.
  • Proposal of efficient algorithms for solving the weighted proximal mapping (WPM).

Main Results:

  • CQNPM demonstrates faster convergence, requiring fewer iterations than traditional APMs.
  • The proposed efficient WPM solvers make CQNPM computationally feasible.
  • Numerical experiments confirm the effectiveness and efficiency of CQNPM for non-Cartesian MRI data reconstruction.

Conclusions:

  • CQNPM offers a significant improvement in convergence speed for CS MRI reconstruction.
  • Efficient WPM solutions are key to the practical application of CQNPM.
  • The method proves effective and efficient for reconstructing complex, non-Cartesian MRI datasets.