The advancement of terahertz (THz) imaging technology has extended its application into the medical field. For example in cancer diagnosis, where it enables differentiation between cancerous and normal tissues, cavities, and other pathological structures. Despite its potential, THz imaging currently falls short in resolution compared to visible light and X-ray imaging, which are standards in clinical diagnostics. Given the critical need for high-resolution imaging in medical diagnostics, enhancing the resolution of THz images is imperative to recover finer structural details. This study proposes an unsupervised method to address the challenge posed by the limited number of THz image samples and the lack of paired high-resolution references. Our algorithm is based on the KernelGAN approach and is designed to address the issue of edge blurring in terahertz images while making the most of the limited THz data available. To achieve this, we incorporate the Sobel operator to extract edge features, enabling us to capture the most critical edge information from the small dataset. To address the lack of high-resolution images in terahertz imaging, we use an improved KernelGAN method to obtain an effective specialized kernel tailored to our terahertz liver cancer dataset. Subsequently, we employ the commonly used unsupervised super-resolution framework- ZSSR, to generate clear high-resolution images. Experimental results demonstrate our method has significant improvements in image quality metrics such as PSNR and SSIM.