Image Denoising Based On Calculus Of Variations And Partial Differential Equations, And Its Fast Algorithm

The obtained images usually are polluted by more or less noises. These noises not only seriously deteriorate the quality of the images and damage some important details characteristics in the images, even the images become very fuzzy. These problems are great challenges for subsequent image processing work. However, Traditional image denoising methods can not meet people’s requirements of high quality and high-definition images. Through more than 20 years development, image denoising method based on partial differential equations has become one of the research hotspots of modern applied mathematics. This paper focuses on image denoising methods based on calculus of variations and partial differential equations, and mainly includes the following contents and innovations:(1) Some denoising methods based on calculus of variations and partial differential equations(P-M model, TV model, adaptive TV model and four-order YK model) are introduced and their advantages and disadvantages are analyzed. In addition, some fast algorithms(dual algorithm, Split Bregman and ADMM algorithm) are described.(2) By analyzing the Poisson noise model(Le model) using the direct method of calculus of variation, a box constraint of the solution to the Le model is given. Furthermore, a fast numerical algorithm to the Le model based on box constraint is developed by incorporating the ADMM algorithm and the convergence of the algorithm is proved. Finally, numerical experiments results show the effectiveness and feasibility of the algorithm.(3) An adaptive denoising model by combining adaptive TV model is presented to remove the Poisson noise. Also, a fast algorithm to the model is developed by incorporating the ADMM algorithm. Finally, numerical experiments results show the effectiveness and of feasibility the algorithm.