Applications Of Convex Optimization Algorithms In Image Processing

With the passage of time,science and technology continue to develop,and a clear image affects all aspects of people's social life,especially in the fields of automatic control,aerospace,and medical imaging.Usually most images contain noise,so the image needs to be denoised or deblurred.For image processing problems,an optimization model of convex optimization problem can be abstracted,and the convex optimization algorithm is used to solve this model,and then the image is processed denoising or deblurring.This paper mainly studies the application of convex optimization algorithm in image processing.Among them,the convex optimization algorithm includes an improved ADMM algorithm and an inexact double primal-dual algorithm for solving saddle point problems.The improved ADMM algorithm based on compressed sensing is improved on the basis of the traditional ADMM algorithm.Combined with compressed sensing theory,the convergence and convergence speed of the improved ADMM algorithm are proved in detail.Finally,the algorithm is applied to image denoising,and the numerical experiments show that the algorithm can be used to solve the problem of image denoising,and the peak signal-to-noise ratio of the improved ADMM algorithm is improved compared with the total variation adaptive algorithm,PDE algorithm and other algorithms.The experimental results show that the improved ADMM algorithm combined with compressed sensing theory can be used to solve the problem of image denoising.The inexact double primal-dual algorithm is based on the double extrapolation primal-dual algorithm,and introduces the inexact algorithm,which adds disturbance to the primal variable and the dual variable respectively.First,the convex optimization problem is converted into a saddle point problem,and then the algorithm is used to solve the saddle point problem,and the convergence and convergence speed of the algorithm are proved in detail.Finally,the inexact double primal-dual algorithm is used in image denoising and deblurring.Numerical experiments have proved that the algorithm can be used to solve image denoising and deblurring problems.Compared with GPDHG algorithm,DEPDA algorithm and other algorithms,the signal-to-noise ratio,time and iterations of the algorithm are improved.Experimental results show the effectiveness of the inexact double primal-dual algorithm for solving image denoising and deblurring problems.