Total variation (TV) regularization has been widely used for ill-posed image processing problems to suppress noise and preserve edge features. However, traditional TV regularization tends to yield the "staircasing artifacts", causing piecewise constant approximation of the true image. To overcome this difficulty, we considered a non-smooth convex optimization model based on regularization method with fractional calculus for several typical image processing problems. A proximal gradient algorithm was developed to overcome the difficulty of non-smoothness for the proposed convex optimization model, and solve the optimization model. Numerical experiments demonstrated that the developed method is effective to preserve texture features of images for image denoising, image deblurring and image super-resolution restoration.
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