  High Resolution (HR) medical images provide rich anatomical structure details
to facilitate early and accurate diagnosis. In MRI, restricted by hardware
capacity, scan time, and patient cooperation ability, isotropic 3D HR image
acquisition typically requests long scan time and, results in small spatial
coverage and low SNR. Recent studies showed that, with deep convolutional
neural networks, isotropic HR MR images could be recovered from low-resolution
(LR) input via single image super-resolution (SISR) algorithms. However, most
existing SISR methods tend to approach a scale-specific projection between LR
and HR images, thus these methods can only deal with a fixed up-sampling rate.
For achieving different up-sampling rates, multiple SR networks have to be
built up respectively, which is very time-consuming and resource-intensive. In
this paper, we propose ArSSR, an Arbitrary Scale Super-Resolution approach for
recovering 3D HR MR images. In the ArSSR model, the reconstruction of HR images
with different up-scaling rates is defined as learning a continuous implicit
voxel function from the observed LR images. Then the SR task is converted to
represent the implicit voxel function via deep neural networks from a set of
paired HR-LR training examples. The ArSSR model consists of an encoder network
and a decoder network. Specifically, the convolutional encoder network is to
extract feature maps from the LR input images and the fully-connected decoder
network is to approximate the implicit voxel function. Due to the continuity of
the learned function, a single ArSSR model can achieve arbitrary up-sampling
rate reconstruction of HR images from any input LR image after training.
Experimental results on three datasets show that the ArSSR model can achieve
state-of-the-art SR performance for 3D HR MR image reconstruction while using a
single trained model to achieve arbitrary up-sampling scales.
