A Frequency Domain Neural Network for Fast Image Super-resolution

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.