Provable Preconditioned Plug-and-Play Approach for Compressed Sensing MRI Reconstruction.

Area of Science:

• Medical Imaging
• Signal Processing
• Computational Science

Background:

• Model-based methods are crucial for compressed sensing (CS) MRI reconstruction.
• Effective priors are essential for describing image statistical distributions in CS MRI.
• Plug-and-play (PnP) frameworks leverage denoising algorithms as priors, with deep learning denoisers showing promise.

Purpose of the Study:

• To accelerate the slow numerical solvers typically used in PnP methods for CS MRI reconstruction.
• To introduce a preconditioned PnP method for faster convergence.
• To provide theoretical guarantees for the fixed-point convergence of the proposed method.

Main Methods:

• Development of a preconditioned plug-and-play (PnP) framework tailored for CS MRI.
• Theoretical analysis and proofs of fixed-point convergence for the PnP iterates.
• Numerical experiments utilizing non-Cartesian sampling trajectories for validation.

Main Results:

• The proposed preconditioned PnP method significantly accelerates convergence compared to standard PnP solvers.
• Demonstrated effectiveness and efficiency of the preconditioned PnP approach in CS MRI reconstruction.
• Validated the fixed-point convergence properties through theoretical proofs.

Conclusions:

• The preconditioned PnP method offers an effective and efficient solution for accelerating CS MRI reconstruction.
• This approach enhances the practical applicability of PnP methods in medical imaging.
• The theoretical convergence proofs support the robustness of the proposed technique.