Aplication Research Of Nonlocal Information And TGV Regularization For Image Processing

Digital image processing technology is widely used in scientific research, social production and life. The development of information engineering, biomedicine and other disciplines are inextricably linked with the image processing technology. The nonlocal method and variational regularization method are widely used in image processing and many good results are obtained, hence many classical models and methods were built up. This dissertation mainly study some mathematical algorithms and models in image processing with nonlocal method and second order total generalized variation(TGV) regularization. The innovation of this article is to present the work of several improved image denoising, zooming and inpainting algorithms. The main work can be summarized as follows:In order to remove the additive gaussian white noise for texture images, a novel denoising model is proposed. This model combines the new multiscale geometric analysis tool—wave atoms and nonlocal total variation regularization scheme. This model well considers the advantages : wave atoms which has the ability of sparse representation of the oscillatory texture images and nonlocal TV version has the ability to handle better textures. Therefore, the denoised images through the new method can avoid pseudo gibbs oscillation phenomenon. Numerical experiments show that the proposed model has the better performance of preserving details than both only wave atoms threshold and nonlocal TV, so together with better visual effects.In order to overcome the drawback that TV tends to produce the staircase effect. Two image zooming models are proposed. One is the improved Chambolle model. In the model, the second order TGV is taken as the regularization term, so the new model can not only zoom the image effectively while removing the noise, but also avoid the staircase effect, the simulative experiments show that the proposed model is better than the Chambolle model and wavelet model in terms of both peak signal to noise ratio and visual effect. The other is based on the wavelet zooming method. A new image zooming model which combines wavelet and second order total generalized variation is proposed. The original image is regarded as wavelet low-frequency band for the zoomed image,and high-frequency band is estimated. Further processing is implemented for the zoomed image using second order total generalized variation. Second order total generalized variation may lead to an absence of the staircase effect as well as keep most details, therefore, the image is reconstructed with high quality. Finally, some experimental results have illustrated that our algorithm not only can achieve better zooming but also can produce very satisfactory denoising effect.Multiplicative noise removal is an important research topic on image processing. Under the assumption that the multiplicative noise follows a Gamma distribution, firstly, a new three-stage method for multiplicative noise removal is proposed. In the first stage log-image is processed by adaptive steer kernel regression. Then in the second stage, the total variation regularization method is used to amend the image obtained. At last, via an exponential function and bias correction, the result is transformed back from the log-domain to the real one. The new method combines the advantages of steer kernel regression and total variation method. Experimental results show that the new method is more effective to filter out multiplicative noise. Secondly, a non-convex total generalized variation regularization model and a non-convex low rank regularization model are proposed. Furthermore, we develop the efficient alterative iteration algorithm for solving the two optimization problems. Numerical experimental results show the better performance of the two algorithms in removing noise while preserving edges information and avoiding the staircase effect.In order to inpaint the images containing cartoons and textures, an improved inpainting model is proposed. Proximal p-norm is used to approximate the 0l-norm of sparse coefficients of two parts of the images. We also derive the proximal forward-backward splitting algorithms to find their solutions. Numerical simulation examples are given to demonstrate our proposed nonconvex method achieves significant improvements over classical1 l sparse method and variation TV method in image inpainting.