The Analysis And Research Of Noisy Image Decomposition Model Based On Chambolle’s Nonlinear Projector

This paper mainly researched the cartoon+texture decomposition of noisy images. The basic idea of the variational method:by using the variational method, the image de-composition problem is converted to energy functional minimization problem, derived the Euler-Lagrange equation, using the negative gradient flow method to obtain the evolution equation, the numerical experiments give the results of the model. With the fast devel-opment of the mathematics and computer science, the study of mathematics and image processing has become a hot spot of current research. Extracted noise or texture from the image is an important task of image processing. In recent years, partial differential method is widely applied to image processing. One way is directly construct, as Perona and Malik raised the heat conduction equation. This method has a lot of options when determining the diffusion coefficient, also has the ability to smooth graphics and sharpen image edges. Another method is through the variational to get a certain kind of energy functional’s Euler-Lagrange equation, then structure the partial differential equation. The latter was first proposed by Rudin-Osher-Fatemi and applied to image denoising in 1992, called the ROF model. In 2009, Li et al. designed a variational denoising model for partly textured images by introducing texture detecting function in the ROF model. In 2012, Liu et al. developed a new model for noisy image decomposition inspired by ROF model and the texture detecting function. In 2011, Chambolle proposed a nonlinear projector algorithm to efficiently solve the ROF model. In 2013, Gilles et al. applied the algorithm to cartoon+texture decomposition model, and achieved a good result.In this paper, we based on the classic ROF model, texture detecting function and Chambolle’s nonlinear projector algorithm, and made the following work:The first, we designed a new model for noisy image decomposition based on Cham-bolle’s nonlinear projector algorithm;Second, our model is applied to the noisy image and noise-free image;Third, our model and other models have made the appropriate comparative study, and put forward their own scope;Fourth, we made a lot of numerical experiments and validated the theoretical results of the models.