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Convergent Complex Quasi-Newton Proximal Methods for Gradient-Driven Denoisers in Compressed Sensing MRI

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This study introduces a faster complex quasi-Newton proximal method for compressed sensing (CS) MRI reconstruction. The novel approach improves convergence speed and theoretical guarantees for model-based CS MRI using gradient-driven denoisers.

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Area of Science:

  • Medical Imaging
  • Computational Imaging
  • Applied Mathematics

Background:

  • Model-based methods are crucial for accurate compressed sensing (CS) MRI reconstruction.
  • Effective image priors are challenging to find for CS MRI.
  • Plug-and-Play (PnP) and REgularization by Denoising (RED) frameworks utilize denoisers as priors.

Purpose of the Study:

  • To develop a faster numerical solver for CS MRI reconstruction using gradient-driven denoisers.
  • To address the theoretical limitations of existing PnP/RED methods with convolutional neural network (CNN) denoisers.
  • To provide a method with rigorous convergence guarantees for non-convex settings in CS MRI.

Main Methods:

  • A novel complex quasi-Newton proximal method is proposed.
  • A modified Hessian estimation ensures Hermitian positive definiteness for complex MRI data.
  • Rigorous convergence analysis is provided for non-convex optimization problems.

Main Results:

  • The proposed method demonstrates faster convergence compared to existing approaches.
  • The method effectively handles the complex domain inherent in CS MRI.
  • Numerical experiments confirm the approach's effectiveness and efficiency on various sampling trajectories.

Conclusions:

  • The developed complex quasi-Newton proximal method offers a significant advancement in CS MRI reconstruction.
  • This work bridges the gap between practical performance and theoretical guarantees for model-based CS MRI.
  • The proposed technique shows promise for accelerating MRI acquisition and improving image quality.