Student's t prior regularization and its application for image restoration
Cong Tang, Liming Tang, Zhuang Fang · Inverse Problems and Imaging · 2025
Variational regularization, renowned for its sound theoretical bases and exemplary performance, is widely used in image restoration. Within the framework of maximum a posteriori (MAP), traditional variational regularization models often utilize Gaussian or Laplace distributions in a specific transformation domain as priors to regularize the restored image. However, the Gaussian distribution is not effective for capturing data with heavy-tailed distributions. While the Laplace distribution has heavy tails, its lack of smoothness in the central region presents computational challenges. To address these problems, we introduce a novel approach called Student's t prior regularization in this paper. Unlike traditional methods, our approach employs the Student's t statistical distribution rather than Gaussian or Laplace one to model the restored images. This allows the model to effectively handle noise and outliers while preserving essential edges and intricate details in the restored image. Moreover, we provide a theoretical demonstration of the existence and uniqueness of solutions for the proposed model. An alternating direction method of multipliers (ADMM) combined with the majorization-minimization (MM) technique is introduced to numerically solve the proposed model. Extensive experiments conducted on different images validate the effectiveness of the proposed model and demonstrate its superiority compared to several state-of-the-art models.