Sparse Regularization And Its Application In Medical Image Restoration

Medical imaging models such as MRI and CT are affected by artifacts and noise.Artifact and noise may make the image quality unable to meet the require-ment of medical images in clinical application.Therefore,the restoration of medical image affected by artifact and noise is an important task of image processing.In this dissertation,an algorithm for image noise reduction and deblurring is presented.The feasibility of the proposed algorithm is verified theoretically and numerically.Minimizing the energy functional composed of fidelity terms is an effective method for image recovery,but the randomness of noise will lead to the problem's ill-posed.To overcome the ill-posedness,appropriate regularization terms should be added.The classical method is the total variation TV model?the regulariza-tion term is the total variation norm?.Although the TV model can restore the image edge,it can not effectively take into account both image noise reduction and edge recovery for images with sparse gradient distribution.In this dissertation,the7)?0<?1?regularization item is added to the minimization model by using the apriori information of medical image gradient sparse.This model can better reduce the noise and restore the edges of the image,but the the addition of7)?0<?1?regularization item will make the problem evolve into a sparse regularization prob-lem with non-convex optimization.In this dissertation,the non-convex problem is dealt with by the half-quadratic splitting algorithm and the alternating direction method of multipliers?ADMM algo-rithm?.The third chapter introduces the half-quadratic splitting algorithm and gives the convergence theorem of the half-quadratic splitting algorithm for non-convex problem.The numerical experiment verifies the effectiveness of the algorithm,and it is found that the restoration effect of each regularization algorithm is related to the gradient distribution of medical image.In order to find a more effective algorith-m,in chapter 4,we use the fast ADMM algorithm to solve the sparse regularization model.Numerical experiments show that the fast ADMM algorithm is superior to the half-quadratic splitting algorithm in image restoration quality.