A convex total generalized variation regularized model for multiplicative noise and blur removal

Multiplicative noise and blur corruptions usually happen in coherent imaging systems, such as the synthetic aperture radar. Total variation regularized multiplicative noise and blur removal models have been widely studied in the literature, which can preserve sharp edges of the recovered images. However, the images recovered from the total variation based models usually suffer from staircase effects. To overcome this deficiency, we propose a total generalized variation regularized convex optimization model. The resulting objective function involves the total generalized variation regularization term, the MAP based data fitting term and a quadratic penalty term which is based on the statistical property of the noise. Indeed, the MAP estimated data fitting term in the multiplicative noise and blur removal model is nonconvex. Under a mild condition, the quadratic penalty term makes the objective function convex. A primal-dual algorithm is developed to solve the minimization problem. Numerical experiments show that the proposed method outperforms some state-of-the-art methods.