# Unsupervised Low-Light Image Enhancement in the Fourier Transform Domain
## 1 Introduction  
Owing to factors such as insufficient lighting and limitations of hardware devices, many images captured in fields like night photography, security surveillance, and medical imaging often suffer from issues such as blurriness, low contrast, and color loss. These low-light images not only make it difficult to discern the specific content of the images, but also, they often lack the crucial details required for computer vision tasks [1; 2]. In recent years, numerous scholars have proposed various methods to address the problem of low-light image enhancement from different perspectives. Traditional methods often rely on handcrafted rules or image processing techniques. [PERSON] et al. [3] applies the hybrid genetic algorithm, which combines the difference and genetic algorithm, to low-light image enhancement. Through the fast search ability of the algorithm, the optimal transform curve can be obtained, and it has better adaptive ability. [PERSON] et al. [4] proposed an adaptive Histogram Equalization method to expand the dynamic range by changing the histogram of the image. However, Histogram Equalization applies a strategy of global adjustment, resulting in local overexposure and amplification of hidden noise. Therefore, on this basis, there are a lot of methods to propose different improvements. [PERSON] et al. [5] proposed the use of average intensity to maintain the uniformity of illumination, and [PERSON] et al. [6] proposed a noise robustness model to further suppress noise. In addition, [PERSON] et al. [7] proposed a new dedistortion model to better maintain color balance. Retinex image enhancement is a computational technique that aims to improve the visual quality of images by separating the reflectance component from the illumination component. The core idea of the Retinex theory [8] is that an image can be decomposedinto its reflectance component and illumination component. Based on the Retinex theory, [PERSON] et al. [9] proposed the Single Scale Retinex (SSR) algorithm, which stretches the dynamic range to some extent using a Gaussian function and considers the reflectance component as the enhancement result. SSR operates on global pixels and does not take into account local overexposure/underexposure. Therefore, the Multi-Scale Retinex (MSR) et al. [10] was introduced as an improvement over SSR. MSR combines different single-scale Retinex outputs to achieve local dynamic range compression. To enhance the adaptability of the model, [PERSON] et al. [11] suggested calculating the weights of SSR adaptively based on the input image. [PERSON] et al. [12] proposed merging different advantages into a single illumination estimation based on multiple derivatives. [PERSON] et al. [13] proposed restoring the initial illumination with a structurally aware prior. Different from traditional methods, machine learning methods leverage large datasets to learn the mapping between low-light images and their enhanced versions. While these methods show promising performance, many of them heavily rely on pairs of low-light/normal-light images [14; 15; 16], which are expensive or even impossible to obtain in real-world scenarios. LLNet [14] is the first deep learning-based low-light image enhancement (LLIE) method, which proposes that one alternative way to cheaply generate such training pairs is to synthesize a low-light image from its counterpart, captured under a normal light condition. RUAS [17] develops a model based on Retinex principles to analyze the inherent under-exposure patterns in low-light images. They also devised a collaborative learning strategy, independent of reference images, which achieves high-performance results while requiring minimal computational resources. Almost all of these methods require a large number of paired images of low-light and normal-light, which take advantage of the powerful learning ability of neural networks; but, it cannot be ignored that its result in overfitting reduces the generalization ability of the model.