Mixed geometry information regularization for image deblurring with multiplicative noise

In this paper, we propose a variational model for the simultaneous removal of multiplicative noise and blur. Variational regularization techniques have been widely employed in various image processing tasks. However, designing models that incorporate sufficient geometric priors remains a challenging problem. To address this issue, we introduce a mixed geometry regularization that integrates both area and curvature terms as priors. Due to the high-order and nonlinear nature of the model, minimizing the associated functional is nontrivial. To overcome this challenge, we adopt the additive operator splitting method and a relaxed scalar auxiliary variable (RSAV) approach, with the latter showing higher computational accuracy for our model. The unconditional stability of these algorithms allows the use of a large time step. Furthermore, we discuss several theoretical properties of the RSAV method. Numerical experiments demonstrate the effectiveness of the proposed model and the efficiency of the corresponding algorithm. Extensive results indicate that our model can effectively address both image deblurring and multiplicative noise removal simultaneously.