Image restoration combining Tikhonov with different order nonconvex nonsmooth regularizations

For piecewise-smooth images with neat boundaries, Tikhonov regularization usually makes images overly smooth, and first order nonconvex nonsmooth regularizations could cause staircase artifacts. Moreover, the image boundaries may be blurred by only utilizing the second difference to reduce staircase artifacts. To overcome above drawbacks, in this paper, piecewise-smooth images with neat boundaries are restored by the GNC method based on combining Tikhonov with different order nonconvex nonsmooth regularizations. This method could both restore the smooth parts and protect the neat boundaries more efficiently. The numerical results are used to show the restored performance of the proposed method.