Research On Weighted And Relaxation Strategies Of The Landweber Iterative Algorithm And Applications

The iterative reconstruction algorithms are the important image reconstruction al-gorithms.The iterative reconstruction algorithms are mainly divided into block iteration and simultaneous iteration.The simultaneous iterative algorithms can be expressed as the weighted Landweber iteration forms.Relaxation strategy and weighting method are important for the iterative convergence speed and the quality of the reconstructed images.This paper studies the weighting and relaxation strategies of the Landweber format iterative algorithm.The main findings and innovations are as follows.1.According to the deduced nice Landweber iteration format,the relaxation s-trategy based on minimizing the spectral radius of the iterative matrix,an accelerated convergence relaxation strategy when only the largest eigenvalue of the iterative matrix is known are proposed.2.The classical Richardson iterative algorithm assumes that the coefficient matrix of a linear system of equations is symmetric positive definite.In this paper,the Richard-son iterative algorithm with positive eigenvalues of coefficient matrix is studied.The convergence is proved and the relaxation strategies are given.3.By analyzing the relationship between the spectral radius of the iterative ma-trix of the Landweber scheme and the condition number of the coefficient matrix,a method of weighting matrix of Landweber scheme is proposed to reduce the condition number of coefficient matrix,to improve the well-posedness of linear equations.The corresponding relaxation strategies are given.The proposed algorithms are applied to CT(Computerized Tomography)image re-construction and electromagnetic tomography(EMT),respectively.In the experiments of CT image reconstructions,the parallel beam scanning simulation model is selected to reconstruct the image using the complete projection data and the limited angle pro-jection data,respectively.The experimental results show that the proposed relaxation strategies and weighted Landweber iterative algorithm can improve the quality of recon-structed images,especially for the limited angle reconstruction.In the experiment of EMT image reconstruction,the simulation experiment and the real data are used to re-construct image respectively.The experimental results show that the proposed weighted Landweber iterative algorithm is effective in improving the quality of the reconstructed images.