Research On Rician Noise Image Restoration Based On Minimization Of Energy Function

Noise is caused by the influence of imaging equipment or interference in signal transmission.Noise image restoration is one of the most active topics in Applied Mathematics and image processing.For different types of noise,many researchers have developed different denoising algorithms.In recent years,with the development and application of nuclear magnetic resonance technology,more and more people pay attention to the problem of Rician noise removal in magnetic resonance imaging.Accordingly,the corresponding Rician noise removal algorithm has been proposed.From the view of mathematical,image denoising is a process of solving an inverse problem.From the view of overall digital image analysis,image denoising is a process of preprocessing noisy image,preparing for subsequent image segmentation and image enhancement.The difficulty of restoring noisy image is to protect the edge and detail information of the original image.The classical model uses image total variation as the regularization term.Although the existing model has achieved good denoising effect,the image is prone to produce virtual edges.To solve this problem,this paper uses the method of using function to express the regularization term,and the classical model is improved from the point of view of energy function minimization.A new Rician noise removal model based on energy function minimization is proposed,and the original dual algorithm is used to solve the model efficiently.Aiming at the theoretical problem of convergence of the algorithm,this paper develops another algorithm of the same model by using the theory of Alternating Direction Method of Multipliers and convex optimization,and achieves similar denoising effect.The main work of this dissertation is as follows:1.A new Rician noise removal model based on energy function minimization is proposed.The classical model uses the total variation of the image as the regularization term.It is easy to generate virtual edges while denoising.Aiming at thisproblem,on the basis of the classical model the new model uses the method of expressing regular terms by functions,and proves that the new model is convex and has unique solution theoretically.2.A fast and efficient original dual Rician noise removal algorithm for solving the new model is developed.Dual algorithm is an effective method to solve the minimization problem,and it occupies less computer memory and has fast convergence speed.The algorithm is applied to solve the new model and good denoising effect is achieved.3.A Rician noise removal algorithm based on ADMM is developed.By establishing the augmented Lagrange equation,the variables are further separated and then iterated to obtain the results of the variables.As we all know,ADMM algorithm is a common tool for solving convex optimization model.The new denoising model proposed in this paper is a convex model.The ADMM algorithm can ensure the theoretical convergence of the algorithm,and also achieves a denoising effect similar to that of the original dual algorithm.