Research And Implementation Of Augmented Lagrangian Algorithm For A New Image Restoration Model

Image restoration is an important research branch in the field of image processing.The purpose is to restore the degraded image to its original appearance and to extract or obtain useful information directly.The augmented Lagrangian method has been widely used in the field of image restoration and computer vision.Based on the variational differential equation theory,the image restoration model for removing salt and pepper noise and Gauss Poisson mixed noise is established in this paper.The numerical algorithm is constructed,and the numerical simulation is given.In this paper,based on the advantages and disadvantages of the general image restoration model,including harmonic model,ROF model,TV-KL model,two new image restoration models are established.Firstly,considering the advantages of harmonic model fidelity term and TV-L1 model,a mixed variational model with L1 fidelity term is proposed to remove the salt and pepper noise with fidelity term,which is solved by augmented Lagrangian algorithm.Numerical simulation is carried out with MATLAB.Experiments show that the proposed new model can effectively remove salt and pepper noise,recover the texture structure information of the image,and the algorithm of the model has higher execution efficiency,and to a certain extent,the"step effect" is suppressed.The maneuverability and validity of the new model are fully proved.Secondly,an image restoration model of mixed L2 and KL fidelity term is presented,which combines the advantages of L2 fidelity term to remove Gauss noise effectively and KL fidelity term to remove Poisson noise effectively.The disadvantage that the harmonic model can't retain the edge information of the image and the TV-KL model can easily cause the "step effect" is overcame.It can effectively remove the Gaussian-Poisson mixed noise.The model is solved by the augmented Lagrangian algorithm.Three sub-problems are divided.To speed up the calculation,we use FFT to solve u operator problem.The experimental results show that the proposed new model can effectively remove the mixed noise,restore the texture structure information of the image,and keep the edge feature of the image better.The superiority of the new model is fully verified.