Wavelet-Based Variational Image Processing Model And Application

In this paper,two models are proposed to overcome the staircase of the WBTVM(wavelet-based total variation(TV) multi-scale) model.Considering the properties of a fourth-order PDE model,we proposed the WBFM(wavelet-based fourth-order PDE multi-scale), firstly.And then combining the WBTVM and WBFM,we propose the WBCM(wave let-based combined multi-scale) model.The WBCM model not only avoid the staircase of WBTVM model,but also overcome the blurring defect of WBFM model.In addition,the exitance and uniqueness of the solution of WBCM is proved.Secondly,two multi-scale parameters determining methods are proposed in this paper. Taking the separate character of signals and noises,we propose an image geometry-adapted (IGA) method for the multi-scale parameters determination.On the basis of IGA method,using the zero-tree wavelet encoder(ZWE),we propose a ZWE method for multi-scale parameters determination,which can modify the multi-scale parameters determined by IGA method.Using the multi-scale parameters determined by the both methods can preserve more edges and fine structures of the image when removing the noise.Furthermore,two fast numerical schemes are proposed,the multi-step time discretization and the "additive operator splitting(AOS)"scheme.Both of them can efficiently accelerate the computing speed,and the multi-step time discretization can also improve the restored quality.In addition,we applied the proposed model in image zooming and image compressing, as example.Lastly,three aspects experiments are given to show the advantages of our models and techniques.The first experiment is to illustrate the good properties in noise removing and sharp edge preserving.The second and the third experiments are used to illustrate the applications in image compressing and zooming,respectively.The matrix multiplicative representation of mask and application will be given in the appendix.