۱٫ Introduction

۲٫ Preliminaries

۳٫ The Proposed Model

۴٫ Experimental Analysis

۵٫ Conclusions

References

Image smooth plays an important role in image pre-processing. For classical image smoothing models, a convex total variation regularizer or a nonconvex regularizer has been widely used to protect image edges and to smooth noise. In this paper, we propose a new effective model in which the total variation regularizer and the nonconvex regularizer are combined to be a new weighted regularizer. The main advantage of our combined regularizer is that some undesirable details such as noise can be removed more effectively, while some important edge details can be preserved better. In addition, an efficient algorithm is designed to solve our model. In our algorithm, an iteratively reweighted process with the Chambolle’s projection algorithm are coupled with each other. Numerical results demonstrate that our proposed model can generate better image smoothing results than those generated by total variation based models and those generated by nonconvex regularizer based models.

Introduction

The nonlinear image smoothing filters such as Anisotropic diffusion filter, Total Variation model, Bilateral filter, NL-means filter, Weighted Least Square filter, can overcome the image blurring problem caused by the linear filters, and smooth the image while protecting the image edges, because those filters utilize prior edge information to remove certain image details and create a scale space representation consisting of simplified image to preserve edges. Anisotropic diffusion filter employs edge-stopping diffusion coefficient to detect edges, so it is able to protect edges from over-smoothing while curbing noise and some unimportant details. Total Variation model is known as its simplicity and high-efficiency which utilizes L1-norm regularization to penalize large gradient magnitudes. Bilateral filters another widely used model can concurrently achieve the goal of detail fattening and edge preservation. Because it takes the geometric distance and the color distance between pixels into consideration in smoothing process. Weighted Least Square filter can overcome some halo artifacts caused by continuous coarsening process due to the model’s robust edge protecting regularization.