Studies On Regularization Models And Algorithms In Image Restoration

During the process of image acquisition, transmission and storage, images are dis-turbed inevitably by the relative movement between imaging device and objective, the diffraction and aberrations of optical system, the nonlinearity of sensitive film, atmo-sphere turbulence and many other external factors, as a result of which, image distortion or artifacts occur in the observed images and the quality of images are seriously reduced. The aim of image restoration is to eliminate or reduce the degeneration effect by these factors on the promise of keeping the image structure and texture as far as possible. The application of image restoration has already infiltrated nanotechnology, astronomy, medical science, visual psychology, remote sensing, security monitoring, digital commu-nication technology and many other fields, and plays an extremely important role in people's life. Therefore, researches about image restoration models and optimization al-gorithms have very important theoretical significance and application value. As two of the common noise in the degradation process, Gaussian noise and impulsive noise have totally different mechanism of action, thus, the corresponding restoration models and solving algorithms under these noises are distinct from each other. In the framework of variational regularization, we study the image restoration problem under Gaussian noise and impulsive noise. The main work and innovative achievements of this thesis are as follows:First of all, we construct a multi-parameter regularization model for deblurring images in the presence of Gaussian noise. After combining total variation which has the property of preserving sharp edges in images with framelet which has adaptive regularity together, we put forward a new image restoration model and take advantage of the accelerated alternating direction method of multipliers to solve this model. Then, multi-parameter regularization model and its solving approach are applied to image denoising, image deblurring and image inpainting and the convergence analysis of the multi-parameter regularization algorithm under some reasonable assumptions is given in our paper. Numerical experiments involving variety of blurs (average blur, Gaussian blur, motion blur and self-defined blur) and different level of noises show that the multi-parameter regularization image restoration model and algorithm are effective and robust to varies of blur kernels and noises in the problems we studied.Moreover, we propose a multi-parameter regularization model for deblurring im-ages in the presence of impulsive noise. After combining total variation which has the property of preserving sharp edges in images with framelet which has adaptive regu-larity together, we put forward a new image restoration model and take advantage of the accelerated alternating direction method of multipliers to solve this model. Then, we introduce an iterative scheme for choosing regularization parameters to this newly proposed multi-parameter regularization algorithm, resulting an adaptive approach for image restoration which is applied to image deblurring and the convergence analysis of the multi-parameter regularization algorithm under some reasonable assumptions is given in our paper. Numerical experiments illustrate that the multi-parameter regular-ization image restoration algorithm is superior to the other state-of-the-art methods in the aspect of reducing stair-casing and preserving sharp edges and textures.Lastly, we put forward a fast dual-based algorithm to solve the dual problem ap-pears in Chambolle's dual method and incorporate an iterative approach for choosing regularization parameter to this newly proposed algorithm for image denoising. Our ex-perimental results show that the quality of these two methods are almost the same but our newly proposed scheme is more efficient than Chambolle's dual method. When they are both used to deal with a synthetic image, the image restoration result by our method is much more better than that by the dual method and the superiority of our newly proposed algorithm will become more apparent with the increasing of the strength of the noise. In addition, Chambolle's dual method is very sensitive to the value of the regularization parameter while our approach is not like this. Numerical experiments show that this adaptively choosing scheme is extremely effective in image denoising and maybe very helpful especially when we have little knowledge about the original image and the noise in it.