求解线性逆问题的谱共轭梯度法

摘要

针对线性逆问题，把原问题的算子方程转化为带有 Tikhonov 正则项的无约束优化问题，提出一个求解线性逆问题的新谱共轭梯度法，并证明算法的全局收敛性。数值结果表明，新算法是有效的。%In this study,a new spectral conj ugate gradient method is presented to solve linear in-verse problems,which are transferred into the linear unconstrained optimization with Tikhonov regularization.The global convergence of the proposed scheme is analyzed.The new algorithm is compared with Landweber,TSVD and TV methods,and numerical results illustrate the effi-ciency of this method.