This work addresses inverse problems in image restoration, focusing on recovering high-quality images from degraded observations, a critical task in fields like microscopy and digital photography. We examine both traditional variational methods and modern deep learning techniques, highlighting hybrid approaches that merge mathematical modeling with data-driven learning. Classical model-based methods use explicit regularization, like total variation, to incorporate prior knowledge and stabilize the inversion process. Meanwhile, deep learning approaches, both supervised and self-supervised, leverage implicit regularization, where network architectures capture and learn prior information from data. We present our recent advancements in this field and discuss the effectiveness of these complementary approaches in solving complex image restoration problems in theory and practice.