Image restoration via combining a fractional order variational filter and a TGV penalty

In this paper, a novel variational model for the restoration of images contaminated with multiplicative noise (also known as speckle) is proposed. It combines a fractional-order total variational (FOTV) filter with a total generalized variation (TGV) penalty. The combined approach uses the advantages of both filters and is able to preserve sharp edges while avoiding the staircase effect in smooth regions, resulting in good restoration. An alternating iterative scheme (AIS) and primal-dual method (PDM) are employed to find the solution to sub-problems of the resulting energy functional efficiently, and then the alternating implementation of AIS and PDM is proposed. Experimental results demonstrate that the recommended model achieves good restoration results both quantitatively and qualitatively in handling the multiplicative noise removal problem. Finally, the proposed model is analyzed and compared with some contemporary models in this field.