Mathematical Model for Image Restoration Based on Fractional Order Total Variation

This paper addresses mathematical model for signal restoration based on fractional order total variation (FOTV) for multiplicative noise. In alternating minimization algorithm the Newton method is coupled with time-marching scheme for the solutions of the corresponding PDEs related to the minimization of the denoising model. Results obtained from experiments show that our model can not only reduce the staircase effect of the restored images but also better improve the PSNR as compare to other existed methods

3D facial data fitting using the biharmonic equation

This paper discusses how a boundary-based surface fitting approach can be utilised to smoothly reconstruct a given human face where the scan data corresponding to the face is provided. In particular, the paper discusses how a solution to the Biharmonic equation can be used to set up the corresponding boundary value problem. We show how a compact explicit solution method can be utilised for efficiently solving the chosen Biharmonic equation. Thus, given the raw scan data of a 3D face, we extract a series of profile curves from the data which can then be utilised as boundary conditions to solve the Biharmonic equation. The resulting solution provides us a continuous single surface patch describing the original face

A note on the dual treatment of higher order regularization functionals

In this paper, we apply the dual approach developed by A. Chambolle for the Rudin-Osher-Fatemi model to regularization functionals with higher order derivatives. We emphasize the linear algebra point of view by consequently using matrix-vector notation. Numerical examples demonstrate the differences between various second order regularization approaches

Image Inpainting and Enhancement using Fractional Order Variational Model

The intention of image inpainting is to complete or fill the corrupted or missing zones of an image by considering the knowledge from the source region. A novel fractional order variational image inpainting model in reference to Caputo definition is introduced in this article. First, the fractional differential, and its numerical methods are represented according to Caputo definition. Then, a fractional differential mask is represented in 8-directions. The complex diffusivity function is also defined to preserve the edges. Finally, the missing regions are filled by using variational model with fractional differentials of 8-directions. The simulation results and analysis display that the new model not only inpaints the missing regions, but also heightens the contrast of the image. The inpainted images have better visual quality than other fractional differential filters

p-Laplace Variational Image Inpainting Model Using Riesz Fractional Differential Filter

In this paper, p-Laplace variational image inpainting model with symmetric Riesz fractional differential filter is proposed. Variational inpainting models are very useful to restore many smaller damaged regions of an image. Integer order variational image inpainting models (especially second and fourth order) work well to complete the unknown regions. However, in the process of inpainting with these models, any of the unindented visual effects such as staircasing, speckle noise, edge blurring, or loss in contrast are introduced. Recently, fractional derivative operators were applied by researchers to restore the damaged regions of the image. Experimentation with these operators for variational image inpainting led to the conclusion that second order symmetric Riesz fractional differential operator not only completes the damaged regions effectively, but also reducing unintended effects. In this article, The filling process of damaged regions is based on the fractional central curvature term. The proposed model is compared with integer order variational models and also GrunwaldLetnikov fractional derivative based variational inpainting in terms of peak signal to noise ratio, structural similarity and mutual information