In this paper, we present a frequency domain neural network for image
super-resolution. The network employs the convolution theorem so as to cast
convolutions in the spatial domain as products in the frequency domain.
Moreover, the non-linearity in deep nets, often achieved by a rectifier unit,
is here cast as a convolution in the frequency domain. This not only yields a
network which is very computationally efficient at testing but also one whose
parameters can all be learnt accordingly. The network can be trained using back
propagation and is devoid of complex numbers due to the use of the Hartley
transform as an alternative to the Fourier transform. Moreover, the network is
potentially applicable to other problems elsewhere in computer vision and image
processing which are often cast in the frequency domain. We show results on
super-resolution and compare against alternatives elsewhere in the literature.
In our experiments, our network is one to two orders of magnitude faster than
the alternatives with an imperceptible loss of performance.

本文介绍了一种基于频域卷积定理的神经网络用于图像超分辨率，该网络采用 Hartley 变换作为替代傅里叶变换消除复数，具有很高的计算效率，并能适用于在计算机视觉和图像处理等其他领域中通常使用频域表示的问题。实验证明，该网络比文献中其他替代品的速度快 1 到 2 个数量级，性能损失微不足道。