A Convergent Generalized Krylov Subspace Method for Compressed Sensing MRI Reconstruction with Gradient-Driven...

Area of Science:

• Medical Imaging
• Computational Science

Background:

• Model-based reconstruction is crucial for compressed sensing (CS) MRI quality.
• Plug-and-Play and Regularization-by-Denoising frameworks use denoisers but lack theoretical guarantees.
• Gradient-driven denoisers offer theoretical advantages but are computationally intensive.

Purpose of the Study:

• To address the computational demands of gradient-driven denoisers in CS MRI.
• To propose an efficient optimization method with theoretical guarantees for CS MRI reconstruction.
• To validate the proposed method's efficiency and accuracy.

Main Methods:

• Introduced a generalized Krylov subspace method (GKSM) to solve the optimization problem.
• Established rigorous convergence guarantees for GKSM, even in nonconvex settings.
• Applied GKSM to compressed sensing MRI reconstruction using spiral and radial data.

Main Results:

• GKSM demonstrated significant computational efficiency compared to existing methods.
• The method achieved accurate reconstructions, validating theoretical predictions.
• Numerical experiments confirmed GKSM's effectiveness for CS MRI.

Conclusions:

• GKSM provides an efficient and theoretically sound approach for CS MRI reconstruction.
• The proposed optimization technique is broadly applicable to linear inverse problems.
• This work advances the field of model-based reconstruction in medical imaging.