# A Frequency Domain Neural Network for Fast Image Super-resolution

arXiv: https://arxiv.org/abs/1712.03037 · HTML: https://mlsanity.com/paper/1712.03037/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2017.

## Built on by (most cited first, 12 of 12)

- [On Measuring and Controlling the Spectral Bias of the Deep Image Prior](https://mlsanity.com/paper/2107.01125/) (2021)
- [Knowledge Distillation Circumvents Nonlinearity for Optical Convolutional Neural Networks](https://mlsanity.com/paper/2102.13323/) (2021)
- [Spatial-Frequency Attention for Image Denoising](https://mlsanity.com/paper/2302.13598/) (2023)
- [Exploring Temporal Dynamics in Event-based Eye Tracker](https://mlsanity.com/paper/2503.23725/) (2025)
- [Local-Selective Feature Distillation for Single Image Super-Resolution](https://mlsanity.com/paper/2111.10988/) (2021)
- [Scalable Event Cloud Network for Event-based Classification](https://mlsanity.com/paper/2412.20803/) (2024)
- [A Frequency Domain Constraint for Synthetic and Real X-ray Image Super Resolution](https://mlsanity.com/paper/2105.06887/) (2021)
- [Frequency Aware Face Hallucination Generative Adversarial Network with Semantic Structural Constraint](https://mlsanity.com/paper/2110.01880/) (2021)
- [Tchebichef Transform Domain-based Deep Learning Architecture for Image Super-resolution](https://mlsanity.com/paper/2102.10640/) (2021)
- [A Scale-Arbitrary Image Super-Resolution Network Using Frequency-domain Information](https://mlsanity.com/paper/2212.04314/) (2022)
- [FiGKD: Fine-Grained Knowledge Distillation via High-Frequency Detail Transfer](https://mlsanity.com/paper/2505.11897/) (2025)
- [Efficient All-in-One Weather Restoration using Spectral Harmonization](https://mlsanity.com/paper/2609.02839/) (2026)

## Abstract (arXiv)

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.