Authors: Jian Wang, Miaomiao Zhang Description: This paper presents DeepFLASH, a novel network with efficient training and inference for learning-based medical image registration. In contrast to existing approaches that learn spatial transformations from training data in the high dimensional imaging space, we develop a new registration network entirely in a low dimensional bandlimited space. This dramatically reduces the computational cost and memory footprint of an expensive training and inference. To achieve this goal, we first introduce complex-valued operations and representations of neural architectures that provide key components for learning-based registration models. We then construct an explicit loss function of transformation fields fully characterized in a bandlimited space with much fewer parameterizations. Experimental results show that our method is significantly faster than the state-of-the-art deep learning based image registration methods, while producing equally accurate alignment. We demonstrate our algorithm in two different applications of image registration: 2D synthetic data and 3D real brain magnetic resonance (MR) images.