Two Regularization Methods For X-ray CT Image Reconstruction

X-ray computed tomography(CT)has the advantages of rapid data collection and high image resolution,so it has been widely used in medical,industrial detection and other fields.However,X-ray radiation has the risk of causing diseases such as cancer.Therefore,reducing the X-ray dose is a common concern of doctors and patients.Reducing the energy of X-ray and the number of projection data are two commonly used methods to reduce the dose of X-ray,which leads to low signal to noise ratio(SNR)projection data and incomplete projection data.Therefore,it is of great significance to study the CT image reconstruction methods from low SNR projection data and incomplete projection data.Total variation(TV)regularization method is a common method for low dose X-ray CT image reconstruction,but this method often leads to"blocky effect"in smooth regions(pseudo boundary),which may lead to misdiagnosis of the disease.In order to overcome"blocky effect"of TV method,this paper puts forward two regularization reconstruction methods.Firstly,this paper presents a regularization reconstruction method for X-ray CT by combining dictionary sparse representation and TV.TV method and dictionary learning method are two common image processing methods,which have their own advantages and disadvantages.We combine the two methods and use the dictionary-based sparse repre?sentation regularization method to eliminate"blocky effect"caused by the TV method.Since the model is non-convex and non-smooth,it is difficult to solve.In this paper,alternating direction method is used to solve three sub-problems.The dictionary learning and representation coefficients are updated by the K-singular value decomposition(KSVD)algorithm,and the reconstruction images are updated by the primal-dual algorithm.Secondly,this paper proposes a CT image reconstruction method based on the dif?ference between Li norm of gradient and L2 norm of gradient(L1-L2).Generally,the reconstruction image can be approximated by the piecewise constant function,that is,the boundary is sparse.L0 norm of gradient is an ideal function to measure sparsity,but it is difficult to solve,L2 norm of gradient(TV)regularization can be used as an approxi-mation of L0 norm of gradient,but it will cause "blocky effect" of reconstruction image.L1-L2 regularization is a new approximation of LO norm of gradient,which is easy to solve.Therefore,this paper proposes a CT image reconstruction method based on the d-ifference between L1 norm of gradient and L2 norm of gradient(L1-L2),which overcomes"blocky effect" of TV regularization method.Because the model is non-convex,with the introduction of auxiliary variable,this paper applies the alternating direction method of multipliers(ADMM)to solve the model.The update of auxiliary variable has closed form solution,and the update of reconstruction image can be obtained by using fast fourier transform(FFT)approximately.Finally,the validity of the proposed models are verified by the experimental results of simulated data and real data.We compared the reconstruction images by filtering back-projection(FBP)algorithm?TV method and proposed methods on different data.The reconstruction results indicate that the reconstruction images by the proposed models have obvious advantages in the mean square error and structural similarity,in addition,the"blocky effect"caused by TV method is avoided visually.The proposed methods will make the reconstruction images have lower noise and clearer structural features.