  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. Our code is
available at https://github.com/jw4hv/deepflash.
