Image Enhancement and Denoising by Forward-and-Backward Fourth Order Partial Differential Equations

Image Denoising Combining the P-M Model and the LLT Model

“…We should find out a way for demonstrating the merits of these two models, at the same time, the shortcoming is suppressed by adjusting the parameter. Considering (14) and (15), we try to create a new model by a convex combination ( )…”

“…As in [19], one can minimize (4) and (8), respectively, by using evolution Equations (14) and (15), and one can discrete (14) with difference scheme, the expression as follows: first, let ∆x and ∆y be the square lattice sizes for the x and y variables, ∆t > 0 be the artificial time step in the descent direction. And…”

“…In this section, we will present numerical results obtained by applying our proposed model to image denoising. For comparison, we also present some results from application of the P-M model (14) and the LLT model (15) to the same images. From the result of experiment, we will utilize the pictures to verify these models, especially demonstrate the advantages of the convex combining model: the new model can reduce the blocky effects and avoid leaving the speckle artifacts.…”

“…Meanwhile, most of the second-order models have a drawback; the drawback is that these models can produce the blocky effects. The authors in [11]- [15] also put forward a variety of fourth-order PDEs models. In the domain with a smooth changed in the intensity value, most of second-order models have a tendency to converge to a piecewise constant image, while the fourth-order PDEs models converge to a piecewise planar image.…”