| Algebraic reconstruction algorithm is an important method for image reconstruction. Algorithm is simple and can implemented easily. We use it to reconstruct an image when the projection datas are missing,especially when there are fewer datas. However, Algebraic reconstruction algorithm which needs large amount of calculations has slow convergence rate. In this paper, we rewrites the ART algorithm as a block format based on the symmetrical structure of a projection ray group as SB-Landweber algorithm.Since the presence of noise in projection data, reconstruction image relies on the iteration order of the rays. Using the symmetrical structure between the projection rays and also between the position of pixels, we select the projection datas under one of a series of symmetry-ray groups as a iteration block matrix. That simplifies the calculation of non-zero coefficient in the projection coefficient matrix.According to the traditional perspective of block iteration, SB-Landweber algorithm can elevate the accuracy of reconstructed image by increasing the angle of rays before and after iteration[24].The main task is to implement the algorithm study of SB-Landweber algorithm. By numerical simulation, we can find the relationship between the accuracy of reconstructed image and the relaxation coefficient also and the weight vector. By numerical simulation experiments, we observe the following conclusion:The greater the relaxation coefficient is, the higher the quality of reconstructed image is. The relaxation coefficientλm are constant. Whenλm close to 2,the quality of image reconstruction is the best. Each ray of a symmetry-ray group has similar importance to the quality of reconstructed image when using SB-ART algorithm to reconstruct an image.DenoteΔω=(Δω1,Δω2,…,Δω8, ),Δωi=0.125-ωi.Whenωi U(1/8;Δωi),‖Δω‖2â†'0,i=1,2,…,8,the reconstruted image has a higher quality,ωis a weight vector of a symmetry-ray group in eight symmetrical directions. |
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