Models And Algorithms Of Image Poisson Denoising And Texture Decomposition

Image denoising is one of the basic problems in image processing.At present,most image denoising models and algorithms study the problem of Gaussian additive noise removal.However,in the fields of medicine and astronomy,images are mainly contaminated by Poisson noise.Poisson noise is non-additive noise,the image denoising method based on additive Gaussian noise cannot be directly used for the Poisson denoising problem,so this dissertation focuses on the image Poisson denoising problem.Image decomposition is a further study of image denoising.Its main purpose is to extract useful information from an image,such as image reflection removal,image dehazing,and texture removal.This dissertation studies the decomposition of images into cartoon component and texture component.The cartoon component refers to the global structural information of the image with piecewise continuous regions and sharp boundaries.The texture component models the locally-patterned of small-scale details,usually with some of periodicity and oscillatory nature.This dissertation mainly discusses two problems of image Poisson denoising and image cartoon texture decomposition.The main contents are as follows:For the problem of image Poisson denoising,this thesis proposes a non-local low-rank matrix Poisson denoising model.The matrix composed of non-local image similar blocks has low rank.The low-rank matrix denoising method based on this prior mainly studies the problem of Gaussian noise removal.Unlike Gaussian noise which has an identical and independent distribution,Poisson noise is signal dependent,which makes the problem more challenging.Using the low-rank prior information of the similar block matrix and applying the maximum a posterior(MAP)estimation,this thesis transforms the Poisson denoising problem into an optimization problem.Since the optimization problem doesn't have closed-form solution,this thesis proposes an alternate iterative minimization algorithm to solve the optimization problem,and analyzes the convergence of the minimization iteration sequence.Numerical experimental results show that the non-local low-rank matrix model proposed in this paper not only effectively removes Poisson noise,but also retains more information of texture and edge.For the problem of image decomposition,this dissertation mainly studies the problem of cartoon and texture decomposition for color images.Meyer model is a classic model of gray-scale image decomposition in which TV norm and G norm are used to describe the image of cartoon component and texture component.In the opponent color space,this dissertation proposes an OTVOG color image decomposition model based on the Meyer image decomposition model.Compared with the RGB color space,the chrominance information and the brightness information of the image in the opponent color space are separated,which has great advantages in distinguishing color boundaries.Based on the L1 norm and L? norm of the vector-valued vector,this dissertation defines the OTV norm and OG norm,which are used to describe the cartoon component and texture component of the image respectively.In order to overcome the numerical calculation difficulties caused by the non-differentiation of OTV norm and OG norm,this thesis transforms them into a dual form through conjugate transformation,and then uses the primal-dual algorithm to obtain the numerical solution.The results of numerical experiments show that the new model proposed in this paper performs well in separating the cartoon component and texture component of color images.In addition,this dissertation proposes a Meyer-OCS model for processing blur image restoring and cartoon texture decomposition based on the OTV-OG model.The cartoon image separated by this model and the restored image have achieved good results in objective evaluation indicators and visual effects.