Matrix completion-informed deep unfolded equilibrium models for self-supervised k $k$ -space interpolation in MRI.

Area of Science:

• Medical Imaging
• Deep Learning
• Signal Processing

Background:

• Self-supervised learning in MRI reconstruction addresses slow acquisition and limited labeled data.
• Existing methods offer effective reconstruction but lack interpretability and theoretical grounding.

Purpose of the Study:

• Introduce a novel self-supervised MRI reconstruction approach.
• Provide stringent theoretical guarantees and interpretable networks.
• Eliminate the need for fully sampled labels.

Main Methods:

• Exploit the relationship between CNNs and structural low-rank models.
• Integrate network parameters into iterative reconstruction.
• Implement an interpretable unfolded model learning gradient descent steps.
• Ensure convergence using a non-expansive mapping.

Main Results:

• Demonstrate efficacy in multi-coil MRI reconstruction.
• Show marked improvements over existing self-supervised and regularization methods.
• Achieve results comparable to supervised learning in specific scenarios.

Conclusions:

• Advance state-of-the-art MRI reconstruction.
• Enhance interpretability of deep learning in medical imaging.