Image restoration technology is a crucial field in image processing and is extensively utilized across various domains. Recently, with advancements in graph convolutional network (GCN) technology, methods based on GCNs have increasingly been applied to image restoration, yielding impressive results. Despite these advancements, there is a gap in comprehensive research that consolidates various image denoising techniques. In this paper, we conduct a comparative study of image restoration techniques using GCNs. We begin by categorizing GCN methods into three primary application areas: image denoising, image super-resolution, and image deblurring. We then delve into the motivations and principles underlying various deep learning approaches. Subsequently, we provide both quantitative and qualitative comparisons of state-of-the-art methods using public denoising datasets. Finally, we discuss potential challenges and future directions, aiming to pave the way for further advancements in this domain. Our key findings include the identification of superior performance of GCN-based methods in capturing long-range dependencies and improving image quality across different restoration tasks, highlighting their potential for future research and applications.