# Unsupervised Low-Light Image Enhancement in the Fourier Transform Domain
## 1 Introduction
Collecting paired images of the same scene in both low and normal light conditions is also sometimes difficult. Unsupervised deep learning-based methods have been developed for image enhancement to eliminate the reliance on paired data. EnlightenGAN [18] uses attention-guided U-net as a generator and uses dual discriminators to guide global and local information. In addition to global and local adversarial losses, the global and local self feature preserving losses are proposed to pre-serve the image content before and after the enhancement. Additionally, the CycleGAN [19] model is an unsupervised image-to-image transformation or translation process that can be applied to image enhancement. These methods adopt generative adversarial networks (GANs) [20], which lie in the concept of adversarial loss that is the key to new unsupervised learning methods. In general, the fundamental tasks of low-light image enhancement are enhancing luminance and denoising [21], but most existing learning-based methods tend to amplify noise while enhancing brightness [22], such as EnlightenGAN [18] and CycleGAN [19]. The solution of some approaches is to enhance the image first and then remove noise; however, it may change the local details and textures of the image in the enhancement stage, which makes it difficult for subsequent denoising algorithms to accurately identify and process the noise. [PERSON] et al. [23] provides a method to deal with noise and brightness in the Fourier transform domain. They have observed that the brightness information of an image is concentrated in the magnitude component after performing the Fourier transform, while the noise primarily resides in the phase component. Although enhancement in the Fourier transform domain successfully avoids amplifying noise during the enhancement of image luminance, it is a supervised learning process that requires paired images and overlooks the degradation process from normal-light to low-light images. Inspired by the method of [PERSON] et al. [23], our approach also enhances images in the Fourier transform domain. In this article, our idea is to enhance the luminance of low-light images in the amplitude domain using the CycleGAN model, which involves an unsupervised image generation process that also includes the process from low-light to normal-light images. In the training process, we concurrently introduce the cycle consistency loss of the spatial domain and feature domain. Considering the issue of color deviation during the style transfer process from low-light images to normal-light images in the CycleGAN model, we additionally incorporate a color constancy loss function into our model. In summary, the contributions of this paper are as follows:  
1. Enhancing luminance using the CycleGAN model in the amplitude domain avoids the issue of amplifying noise, and we use the convolution neural network to denoise during the phase domain at the same time. Our model also considers the degradation process from normal-light to low-light images, which can simulate the real environment and expand the training dataset so that the method can better adapt to the image processing task under low-light conditions. 2. We incorporate the cycle consistency loss functions both in the space domain and the Fourier transform domain, which can provide more training signals and help to accelerate the convergence and stability of the training process. The spatial domain cycle consistency loss function allows for a direct comparison of pixel differences between the generated images and the original images. This evaluation enables an assessment of the quality of the generated images at the pixel level. Meanwhile, the cycle consistency loss function in the Fourier transform domain enables the similarity of brightness information.