K-UNN: k-Space Interpolation With Untrained Neural Network
This work addresses MRI reconstruction challenges for medical imaging, offering a method that enhances performance in common scenarios like partial Fourier sampling, though it appears incremental by building on existing untrained neural network approaches.
The authors tackled the problem of MRI reconstruction from undersampled k-space data by proposing a safeguarded k-space interpolation method using an untrained neural network with physical priors, achieving improved accuracy over traditional and supervised deep learning methods in some cases.
Recently, untrained neural networks (UNNs) have shown satisfactory performances for MR image reconstruction on random sampling trajectories without using additional full-sampled training data. However, the existing UNN-based approach does not fully use the MR image physical priors, resulting in poor performance in some common scenarios (e.g., partial Fourier, regular sampling, etc.) and the lack of theoretical guarantees for reconstruction accuracy. To bridge this gap, we propose a safeguarded k-space interpolation method for MRI using a specially designed UNN with a tripled architecture driven by three physical priors of the MR images (or k-space data), including sparsity, coil sensitivity smoothness, and phase smoothness. We also prove that the proposed method guarantees tight bounds for interpolated k-space data accuracy. Finally, ablation experiments show that the proposed method can more accurately characterize the physical priors of MR images than existing traditional methods. Additionally, under a series of commonly used sampling trajectories, experiments also show that the proposed method consistently outperforms traditional parallel imaging methods and existing UNNs, and even outperforms the state-of-the-art supervised-trained k-space deep learning methods in some cases.