非线性体效应的逆问题

非线性体效应在计算机断层扫描重构的理论与应用中,仍然是一个悬而未决的问题.本文利用优化重构算法来解决非线性体效应,建立了离散非线性X射线投影变换模型,将X射线投影变换的逆问题变为一个非凸的优化问题,通过裁剪原用于求解凸优化问题的一阶原对偶算法,提出非线性迭代重构算法来解决非凸问题.通过构建成像系统模型对算法的收敛性和重...

Inverse Problem in Non-linear Partial Volume Effect

Non-linear partial volume effect is still an unsolved problem in the theory and application of computed tomography reconstruction.In this work,an optimization-based reconstruction algorithm for effectively solving this effect was studied and developed.The discrete non-linear X-ray projection transformation model was established,when the inverse problem of X-ray projection transformation was transformed into a non-convex optimization.A non-linear iterative reconstruction algorithm was formulated to solve the non-convex optimization problem by tailoring the first-order primal-dual algorithm developed originally for solving convex optimization problems.Using computer-simulation studies,the convergence and reconstruction accuracy of the algorithm was demonstrated in this investigation.Images reconstructed were examined first through visual inspection with extremely narrow display window for revealing a contrast level of less than 1%,and then assessed with quantitative metrics such as the normalized l2-norm of the difference relative to its truth images.The simulation results show that the nonlinear reconstruction algorithm can converge to the real image within the range of calculation accuracy,and the reconstructed image can also be displayed for the details with image contrast less than 1%.This would provide a reference for the design of computed tomography imaging application algorithm which can effectively compensate the non-linear partial volume effect artifacts.