MRI Reconstruction by Completing Under-sampled K-space Data with Learnable Fourier Interpolation

Abstract

Magnetic resonance imaging (MRI) acceleration is usually achieved by data undersampling, while reconstruction from undersampled data is a challenging ill-posed problem for data-missing and noisy measurements introduce various artifacts. In recent years, deep learning methods have been extensively studied for MRI reconstruction, and most of work treat the reconstruction problem as a denoising problem or replace the regularization subproblem with a deep neural network (DNN) in an optimization unrolling scheme. In this work, we proposed to directly complete the missing and corrupted k-space data by a specially designed interpolation deep neural networks combined with some convolution layers in both frequency and spatial domains. Specifically, for every missing and corrupted frequency, we use a K- nearest neighbors estimation with learnable weights. Then, two convolution neural networks (CNNs) are applied to regularize the data in both k-space and image space. The proposed DNN structures have clear interpretability for solving this undersampling problem. Extensive experiments on MRI reconstruction with diverse sampling patterns and ratios, under noiseless and noise settings demonstrate the accuracy of the proposed method compared to other learning based algorithms, while being computationally more efficient for both training and reconstruction processes.