Autoregressive Heteroscedasticity Modeling Of Images And Its Application In Restoration

Nowadays,digital images are widely applied in people's real life,such as in the field of intelligent transportation,aerospace,medical image and so on.However,due to the problems of imaging equipment or artificial shooting,as well as the effect of noise in the compression and transmission process,the quality of the image will inevitably degenerate and lose a lot of important information.Therefore,image restoration as a basic problem in the field of vision has attracted the attention of many scholars.There are many kinds of image restoration methods now.If we have a certain understanding of the degraded image,we can establish a mathematical model as a priori knowledge,and this method can often get better results.However,people find that the restored image will always lose many important texture structures,and how to restore the image effectively with the condition of maintaining the details of the image and the clear edge structure,is still one of the difficult problems to be solved in this field?As a very useful prior knowledge,gradient distribution of images has been widely applied in image processing technologies.In the past,many scholars used Gauss model,Laplasse model,mixed Gauss model,or super Laplasse model to fit the gradient distribution of natural images.However,the gradient distribution of natural images has the characteristics of "peak and thick tail".These models can not fit the distribution well,and the restoration method based on these models will smooth out many important details of the image,thus reducing the quality of the restored image.Here,this article proposes to use a new model to fit the gradient distribution of natural images.The two-dimensional generalized autoregressive heteroscedasticity model(2D-GARCH)is extended from the GARCH model,and the GARCH model is widely used in the financial field to fit the distribution characteristics of the "peak and thick tail" of the time series.The charact eristic of the two-dimensional generalized autoregressive heteroscedasticity model(2D-GARCH)is that the variance of each pixel in the image is changed,and the current conditional variance is determined by the pixel values of adjacent images and the adjacent variance.This coincides with the related characteristics of natural image gradients.The article mainly discusses the following content.(1)Using the variable step fruit fly optimization algorithm(VS-FOA)to solve the parameters of the model.By reducing the step size at the end of iteration,the algorithm can achieve higher accuracy.The experimental results show that,compared to the traditional fruit fly optimization algorithm,the variable step size of the fruit fly algorithm can find the optimal model parameters faster and obtain higher applicability function values.(2)Then we use different models to model the gradient distribution of images.We compare the kurtosis,the mean square difference and the skewness between the fitting curves of these different models.The experimental results show that the similarity between the fitting results of the 2D-GARCH model and the original gradient distribution is higher.Then,we use the Kolmogorov-Smirnov double-sample test(double sample K-S test)to prove that the 2D-GARCH model and the original gradient distribution are subject to the same distribution.Therefore,the 2D-GARCH model can be used as a priori model of image gradient distribution and applied in image processing.(3)We use 2D-GARCH to design a maximum a posteriori estimator(MAP)to restore degraded images and get good results.We compare the restoration results of our algorithm with other methods.The experimental results show that our method can obtain higher signal to noise ratio(SNR)and structural similarity(SSIM),and can keep the detail texture and edge structure in the original image very well.