The main purpose of low-light image enhancement (LLIE) is to improve the quality of images captured in low-light environments, ensuring visibility and preserving details. How to balance global illumination and local details enhancement, as well as effectively suppress noise, remains the main challenges currently faced. To address these issues, we propose a two-stage LLIE method termed as IEDNet, where the first stage aims to enhance illumination in the spatial domain and the second stage aims to remove noise in the frequency domain. In the first stage, we design a multi-scale illumination enhancement (MIE) module to enhance global illumination and local details. In MIE, we propose a multi-scale feature aggregation (MFA) block that performs multi-scale feature enhancement and aggregation, which can obtain richer feature representations and capture more context and detail information. Although we conduct effective illumination enhancement in the first stage, some noise is introduced during the enhancement process. Therefore, in the second stage, we design a wavelet-based frequency-aware denoising (WFD) module to further remove noise from the image and obtain better enhancement results. We conduct extensive experiments to validate our design and demonstrate on seven benchmark datasets that it achieves state-of-the-art (SOTA) methods both quantitatively and qualitatively.