Landweber Iterative Algorithms For Angle-limited Image Reconstruction And Its Implementation Studies

The Landweber scheme is an algebraic reconstruction method and includes several important algorithms as its special cases.The convergence of the the Landweber scheme is of both theoretical and practical importance.A general iterative scheme for angle-limited image reconstruction based on Landweber's method was introduced and its convergence conditions were established[2].In this thesis,we study the algorithm implements and relaxation strategies,and show the efficiency of this algorithm through the numerical simulation.The problem of angle-limited image reconstruction belongs to incomplete data.It is far-ranging used in areas which include medical tomography,seismic tomography, radio astronomy,electron microscopy and so on.This problem mainly discusses the angleθ,0≤θ≤θ₀＜πof Radon transformRf(p,θ)=(?) f(p cosθ-s sinθ,p sinθ+ s cosθ)dsIn this part we make a study of angle-limited image reconstruction,we transfer this problem into band-limited function extrapolation,and give the Landweber iterative methods for angle-limited image reconstruction.We choose different relaxation coefficients,from the numerical simulation,we show the efficiency of this algorithm.This article's main task is to implement the algorithm study of the Landweber iterative scheme for angle-limited image reconstruction which based on the work in[2]. We study the relaxation strategies from the numerical simulation.We choose different relaxation coefficientλ_n and the angleθ₀,from the numerical simulation,we have the conclusion that whenλ_n close to 1,the efficiency of image reconstruction is the best.At the same time as the angleθ₀ increases,the reconstruction of the image gradually change better.