Terahertz imaging technology shows great potential in cancer diagnosis. However, due to absorption, scattering in biological tissues, and limitations in device sensitivity, terahertz imaging often comes with various noises. To improve the quality of terahertz imaging, denoising techniques are crucial for addressing noise issues. By reducing noise, the structures and features of cancerous regions can become clearer, thereby contributing to the improvement of diagnostic outcomes. However, in recent years, deep learning algorithms have achieved significant results in image denoising, but deep learning based denoising algorithm typically require paired clean and noisy images for training, which are not available in our dataset. In this paper we propose a self-supervised single-image denoising method for our THz liver cancer datasets. On one hand, due to the absence of paired images, we generate noisy image pairs through diagonal pixel down-sampling. On the other hand, to enable the model to learn more accurate and relevant semantic information from terahertz images with substantial noise, we introduce a regularization term. Experimental results demonstrate that our terahertz denoising method significantly improves the quality of terahertz imaging, effectively reduces noise, and enhances the visibility of cancerous regions, providing beneficial support for accurate liver cancer diagnosis.