IEEE Trans Med Imaging. 2020 Feb;39(2):377-386. doi: 10.1109/TMI.2019.2927101. Epub 2019 Jul 5.
The annihilating filter-based low-rank Hankel matrix approach (ALOHA) is one of the state-of-the-art compressed sensing approaches that directly interpolates the missing k -space data using low-rank Hankel matrix completion. The success of ALOHA is due to the concise signal representation in the k -space domain, thanks to the duality between structured low-rankness in the k -space domain and the image domain sparsity. Inspired by the recent mathematical discovery that links convolutional neural networks to Hankel matrix decomposition using data-driven framelet basis, here we propose a fully data-driven deep learning algorithm for k -space interpolation. Our network can be also easily applied to non-Cartesian k -space trajectories by simply adding an additional regridding layer. Extensive numerical experiments show that the proposed deep learning method consistently outperforms the existing image-domain deep learning approaches.
基于湮灭滤波器的低秩 Hankel 矩阵方法 (ALOHA) 是最先进的压缩感知方法之一，它直接使用低秩 Hankel 矩阵完成来内插缺失的 k-空间数据。ALOHA 的成功归功于 k-空间域中简洁的信号表示，这得益于 k-空间域和图像域稀疏性之间的结构低秩性的对偶性。受最近的数学发现的启发，该发现使用基于数据的帧状基将卷积神经网络与 Hankel 矩阵分解联系起来，我们在这里提出了一种用于 k-空间插值的完全基于数据的深度学习算法。我们的网络还可以通过简单地添加额外的重新网格化层，轻松应用于非笛卡尔 k-空间轨迹。大量的数值实验表明，所提出的深度学习方法始终优于现有的图像域深度学习方法。
