Accelerating Cartesian MRI by domain-transform manifold learning in phase-encoding direction.

This study developed a domain-transform framework comprising domain-transform manifold learning with an initial analytic transform to accelerate Cartesian magnetic resonance imaging (DOTA-MRI). The proposed method directly transforms undersampled Cartesian k-space data into a reconstructed image. In Cartesian undersampling, the k-space is fully or zero sampled in the data-acquisition direction (i.e., the frequency-encoding direction or the x-direction); one-dimensional (1D) inverse Fourier transform (IFT) along the x-direction on the undersampled k-space does not induce any aliasing. To exploit this, the algorithm first applies an analytic x-direction 1D IFT to the undersampled Cartesian k-space input, and subsequently transforms it into a reconstructed image using deep neural networks. The initial analytic transform (i.e., 1D IFT) allows the fully connected layers of the neural network to learn 1D global transform only in the phase-encoding direction (i.e., the y-direction) instead of 2D transform. This drastically reduces the number of parameters to be learned from O(N) to O(N) compared with the existing manifold learning algorithm (i.e., automated transform by manifold approximation) (AUTOMAP). This enables DOTA-MRI to be applied to high-resolution MR datasets, which has previously proved difficult to implement in AUTOMAP because of the enormous memory requirements involved. After the initial analytic transform, the manifold learning phase uses a symmetric network architecture comprising three types of layers: front-end convolutional layers, fully connected layers for the 1D global transform, and back-end convolutional layers. The front-end convolutional layers take 1D IFT of the undersampled k-space (i.e., undersampled data in the intermediate domain or in the ky-x domain) as input and performs data-domain restoration. The following fully connected layers learn the 1D global transform between the ky-x domain and the image domain (i.e., the y-x domain). Finally, the back-end convolutional layers reconstruct the final image by denoising in the image domain. DOTA-MRI exhibited superior performance over nine other existing algorithms, including state-of-the-art deep learning-based algorithms. The generality of the algorithm was demonstrated by experiments conducted under various sampling ratios, datasets, and noise levels.