Research On Fast Algorithm Of The Fractional Order Total Variation Model

Images,as one of the most common things in human life,are also the main source for people to get information.However,in the process of image acquisition and processing,the image is more or less polluted by noise,which not only affects the quality of the image,but also makes the post processing work more difficult.Image denoising is a kind of image preprocessing technology.Image denoising is the most basic and core problem in image processing.At present,the total variation(TV)denoising model is better than the other denoising models.It has a good deal with the edge and smooth region of the image,but there are some small shortcomings.This denoising model can easily remove a lot of texture parts.After denoising,the image will have staircase effect.Aiming at the problems of TV model denoising,people have developed many improved models based on it,such as higher-order model,adaptive TV model and so on.In this paper,the fractional TV model is studied,and the Majorization-minimization(MM)algorithm is applied to the fractional order TV model,and the improved new algorithm is used to denoise the image in order to get the desired results.Through the results of the experiments,it can be seen from the comparison that the algorithm presented in this paper has better denoising ability when dealing with some one-dimensional signals,and it also has a good performance on the processing of two-dimensional signals.The main contents and innovation points of this paper include the following aspects:firstly,starting with the fractional derivative and the total variation model,this paper introduces the definitions of the three fractional derivatives and the relation between them,and gives the expression of the total variation model and several algorithms.Secondly,the fractional order total variation model and its algorithms are presented.Combined with the previous MM algorithm,this paper gives the MM algorithm of the FTV model.Finally,the experiments are given and the experimental results are compared and analyzed,thus the conclusion is drawn.