Guided depth super-resolution (GDSR) is an essential topic in multi-modal image processing, which reconstructs high-resolution (HR) depth maps from low-resolution ones collected with suboptimal conditions with the help of HR RGB images of the same scene. To solve the challenges in interpreting the working mechanism, extracting cross-modal features and RGB texture over-transferred, we propose a novel Discrete Cosine Transform Network (DCTNet) to alleviate the problems from three aspects. First, the Discrete Cosine Transform (DCT) module reconstructs the multi-channel HR depth features by using DCT to solve the channel-wise optimization problem derived from the image domain. Second, we introduce a semi-coupled feature extraction module that uses shared convolutional kernels to extract common information and private kernels to extract modality-specific information. Third, we employ an edge attention mechanism to highlight the contours informative for guided upsampling. Extensive quantitative and qualitative evaluations demonstrate the effectiveness of our DCTNet, which outperforms previous state-of-the-art methods with a relatively small number of parameters. The code is available at https:// github.com/Zhaozixiang1228/GDSR-DCTNet