Sparse representation for restoring images by exploiting topological structure of graph of patches

Image restoration poses a significant challenge, aiming to accurately recover damaged images by delving into their inherent characteristics. Various models and algorithms have been explored by researchers to address different types of image distortions, including sparse representation, grouped sparse representation, and low-rank self-representation. The grouped sparse representation algorithm leverages the prior knowledge of non-local self-similarity and imposes sparsity constraints to maintain texture information within images. To further exploit the intrinsic properties of images, this study proposes a novel low-rank representation-guided grouped sparse representation image restoration algorithm. This algorithm integrates self-representation models and trace optimization techniques to effectively preserve the original image structure, thereby enhancing image restoration performance while retaining the original texture and structural information. The proposed method was evaluated on image denoising and deblocking tasks across several datasets, demonstrating promising results.