Research On Color Image Compression Based On A Class Of Reaction-Diffusion System

In recent years,with the continuous development of multimedia products,people's demands are growing faster and faster.The problem of insufficient network bandwidth and storage capacity is becoming more and more obvious.If we want to reduce the image storage space and speed up the transmission rate,we need to compress the image.The purpose of image compression is to reduce redundant information in images and store or transfer data in an efficient form,so that we can use less image information to achieve the same visual effect.Image compression can be divided into lossless compression and lossy compression according to the decompression effect.Generally,lossy compression algorithm is studied.In order to reduce the color penetration that occurs during decompression,this paper mainly studies the lossy compression algorithm of color images based on a class of linear reaction-diffusion equations,and the main work accomplished is as follows:Firstly,according to the viewpoint of differential geometry,the image in the RGB color space is regarded as the hypersurface of three-dimensional Euclidean space.Through analysis,the first basic form of hypersurface is equivalent to the sum of squares of image gray value change.Accordingly,we proposed an energy functional in chapter 3.The existence and uniqueness of energy functional minimum point is proved,and then the isotropic reaction diffusion equations corresponding to energy functional are derived by means of gradient descent flow method,the existence and uniqueness of weak solutions of the reaction diffusion equations are proved,and the finite-difference scheme is given.In order to apply the proposed model to image compression,in the process of selecting representative pixels,a local optimal algorithm is applied to extract representative pixel points of R,G,and B channels.The pixel values and locations of the selected representative pixels are then stored.After decompressing the image,the results of the isotropic reaction-diffusion equation model image processing are compared with other compression algorithms.Through the experimental results,the image shows the importance of the selected structural features.The first basic matrix corresponding to vector image also contains abundant structural information.In order to apply it to image compression,an energy functional based on the first basic matrix is proposed in chapter 4.Through the gradient descent flow method,the anisotropic reaction diffusion equations corresponding to the energy functional are derived.Its theoretical proof is similar to the case of isotropic.In addition,the numerical scheme with rotation invariance for the anisotropic reaction-diffusion equations is given.The time step of this scheme is 3-4 times that of the finite-difference scheme,which greatly improves the computational efficiency.Applying the model to image compression,the processing results show that the selected structural features can reduce the color bleeding phenomenon of other algorithms when decompressing the image.