A Convex Variational Model for Restoring Blurred Images with Large Rician Noise

In this paper, a new convex variational model for restoring images degraded by blur and Rician noise is proposed. The new method is inspired by previous works in which the non-convex variational model obtained by maximum a posteriori estimation has been presented. Based on the statistical property of Rician noise, we put forward to adding an additional data-fidelity term into the non-convex model, which leads to a new strictly convex model under mild condition. Due to the convexity, the solution of the new model is unique and independent of the initialization of the algorithm. We utilize a primal–dual algorithm to solve the model. Numerical results are presented in the end to demonstrate that with respect to image restoration capability and CPU-time consumption, our model outperforms some of the state-of-the-art models in both medical and natural images.