Deep Manifold Learning for Dynamic MR Imaging

Recently, low-dimensional manifold regularization has been recognized as a competitive method for accelerated cardiac MRI, due to its ability to capture temporal correlations. However, existing methods have not been performed with the nonlinear structure of an underlying manifold. In this paper, we propose a deep learning method in an unrolling manner for accelerated cardiac MRI on a low-dimensional manifold. Specifically, a fixed low-rank tensor (Riemannian) manifold is chosen to capture the strong temporal correlations of dynamic signals; the reconstruction problem is modeled as a CS-based optimization problem on this manifold. Following the manifold structure, a Riemannian gradient descent (RGD) method is adopted to solve this problem. Finally, the RGD algorithm is unrolled into a neural network, called Manifold-Net, on the manifold to avoid the long computation time and the challenging parameter selection. The experimental results at high accelerations demonstrate that the proposed method can obtain improved reconstruction compared with three conventional methods (k-t SLR, SToRM and k-t MLSD) and three state-of-the-art deep learning-based methods (DC-CNN, CRNN, and SLR-Net). To our knowledge, this work represents the first study to unroll the iterative optimization procedure into neural networks on manifolds. Moreover, the designed Manifold-Net provides a new mechanism for low-rank priors in dynamic MRI and should also prove useful for fast reconstruction in other dynamic imaging problems.