Image Denoising And Colorization Based On Calculus Of Variations And Partial Differential Equations

Image denoising and image colorization are two important research contents in the field of image processing.Image denoising is to remove the noise in the image.Noise which affects the image quality comes from the interference information in the process of image transmission.Image denoising is the basis of image processing.Image colorization is generically used to describe the process of converting a grayscale image into a color image.The emergence of colorization enables people to extract more accurate information from images,which is beneficial for people to deeply understand the image content.Colorization can be applied for ancient painting restoration,medical grayscale image colorization,etc.This paper studies image denoising methods based on partial differential equations and image colorization methods based on total variation.The main research contents and innovations are as follows.For the image denoising problem,the method of partial differential equations is one of the research directions.The second-order partial differential equation can effectively retain the image boundaries while denoising,but"staircase effect"usually occurs in the denoised image.In order to solve the"staircase effect",this paper proposes two new fourth order partial differential equation image denoising model.The model uses the finite difference method for numerical calculation,and then MATLAB simulation experiments are performed on different images.We use the peak signal to noise ratio,signal to noise ratio and mean structure similarity as a criterion to measure the quality of an image.In the experiment,the first model is based on the method of manual debugging threshold,and the second model is programmed to realize the adaptive threshold selection based on histogram.The experimental analysis results show that the two new models can effectively remove the multiplicative noise and preserve the image edges.For the image colorization problem,the existing colorization methods often have the phenomenon of color bleeding or uneven colorization.For color images,the coupling way between channels also affects the image colorization effect.In order to solve the problem of coupling between multiple channels in image colorization and prevent the color bleeding phenomenon,this paper proposes a new image colorization model based on the natural vectorial total variationTV_J in YCbCr color space.TV_J supports a common edge direction for all channels,it leads to a better preservation of color edges.At the same time,the proposed model is a convex model in the YCbCr color space,which is not sensitive to the initial value and has good robustness.We give the existence of the minimizer of the proposed model and use primal-dual algorithm to numerically solve this model,then illustrate the convergence of the algorithm.Finally,the peak signal to noise ration,mean square error,mean structure similarity index,and quaternion structural similarity are used for numerical comparison.Compared with other models,the proposed model can preserve the contours well and reduce color bleeding effects at edges,which has certain advantages compared both on structure images and texture images.