Image Denoising And Projection Reconstruction Based On Fractional Derivative

Image denoising and image reconstruction from projection are two important directions in image processing.They play an important role both in theory and practice.In this paper,we propose a variational framework which uses a combination of total variation and fractional-order derivatives in the regularization term of the objective function.Besides,we introduce a convenient edge detector to detect edges.Numerical experiments show the effect of this model,which is also able to avoid the staircase effect.For image reconstruction from projection,we discuss an adaptive regularization approach for density reconstruction of axially symmetric object whose tomography comesfrom a single X-ray projection.The method we proposed is based on the combination of total variation and Laplace operator.By the use of adaptive technology,the weight of the regularization can be automatically adjusted.Its main advantage is that it can reduce the staircase effect in smoothly varying regions while keeping sharp edges.Moreover,it improves the result and simplifies the use of parameters.We apply the augmented Lagrangian method to solve the optimization involved.Numerical results show that the proposed method has improved the accuracy of density edges and reconstruction results.Besides,the method is not sensitive to the measured data noise.