基于拟解的正则化参数选取法

A Method for Choosing the Regularization Parameters Based on the Quasi-solution

线性不适定问题中Tikhonov正则化参数的有效选取一直是反问题领域研究的重要问题。在模型函数框架下,考虑了用显式迭代法求解一类拟解的近似方程,从而得到了Tikhonov正则化参数的近似选取。对于这种近似选取,在传统模型函数下基于拟解方程提出了选取正则化参数的新算法,并得到该算法的局部收敛性。最后,给出了求解不适定问题的数值实现,说明了算法的有效性。

Research on choosing Tikhonov regularization parameters in linear ill-posed problems is an important field in inverse problem.Consider an approximation of the Tikhonov regularization parameters under the model function framework,which solves an approximate quasi-solution equation with an explicit expression iteratively.For this approximation,a new algorithm for determining regularization parameters based on the traditional model function and quasi-solution equation is proposed,which is proven to be local convergent.Numerical implementations for ill-posed problems are presented to illustrate the validity of the proposed algorithm.