K-UNN: k-space interpolation with untrained neural network

Area of Science:

• Medical Imaging
• Artificial Intelligence
• Signal Processing

Background:

• Untrained neural networks (UNNs) show promise for MR image reconstruction without training data.
• Existing UNNs lack physical prior modeling, limiting performance in scenarios like partial Fourier (PF) and regular sampling, and lack theoretical guarantees.

Purpose of the Study:

• To develop a safeguarded k-space interpolation method for MRI reconstruction.
• To integrate physical priors into UNN-based MRI reconstruction for improved accuracy and theoretical guarantees.

Main Methods:

• A specially designed UNN with a tripled architecture was developed.
• The UNN is driven by three physical priors: transform sparsity, coil sensitivity smoothness, and phase smoothness.
• A safeguarded k-space interpolation technique was employed.

Main Results:

• The proposed method effectively characterizes physical priors in MR images.
• Guaranteed tight bounds for interpolated k-space data accuracy were proven.
• The method consistently outperformed traditional parallel imaging and existing UNNs.
• Performance was competitive with supervised deep learning methods in PF and regular undersampling.

Conclusions:

• The proposed safeguarded k-space interpolation method with a physics-informed UNN significantly improves MRI reconstruction.
• This approach offers theoretical guarantees and robust performance across various undersampling scenarios, outperforming existing methods.