Equilibrated Zeroth-Order Unrolled Deep Network for Parallel MR Imaging.

Area of Science:

• Medical Imaging
• Artificial Intelligence
• Deep Learning

Background:

• Model-driven deep learning unrolls iterative algorithms into cascade networks using network modules instead of first-order information.
• Existing methods lack theoretical guarantees for functional regularizer existence and global convergence/robustness of unrolled networks.

Purpose of the Study:

• To propose a safeguarded methodology for network unrolling in parallel MRI reconstruction.
• To ensure network outputs align with regularization models and guarantee robustness.

Main Methods:

• Unrolling a zeroth-order algorithm where the network module acts as a regularizer.
• Employing a deep equilibrium model-inspired approach for fixed-point convergence before backpropagation.
• Proving network robustness against noisy measurement data.

Main Results:

• The proposed network tightly approximates actual MR images.
• The network demonstrates robustness against noisy interferences.
• Numerical experiments show superior performance compared to traditional and unrolled deep learning MRI reconstruction methods.

Conclusions:

• The safeguarded network unrolling methodology provides theoretical guarantees for convergence and robustness in parallel MRI.
• This approach enhances MRI reconstruction accuracy and reliability, outperforming existing state-of-the-art techniques.