论文标题
Tikhonov功能具有正规化中引入的公差度量的功能
Tikhonov functionals with a tolerance measure introduced in the regularization
论文作者
论文摘要
我们考虑了修改的Tikhonov型功能，可用于解决方案不良的非线性逆问题。在生产工程领域的应用中，我们允许解决方案中的小偏差，这些偏差是通过功能的正则化项中的公差度量来建模的。对于这种功能以及Bregman距离中的收敛速率证明了最小化器的存在，稳定性和弱收敛性。我们提供了一个示例，用于说明公差对正则化解决方案的影响，并检查参数选择规则，以找到假定公差值的最佳正则参数。此外，我们讨论了将公差纳入正规化功能时重建稀疏溶液的前景。
We consider a modified Tikhonov-type functional for the solution of ill-posed nonlinear inverse problems. Motivated by applications in the field of production engineering, we allow small deviations in the solution, which are modeled through a tolerance measure in the regularization term of the functional. The existence, stability, and weak convergence of minimizers are proved for such a functional, as well as the convergence rates in the Bregman distance. We present an example for illustrating the effect of tolerances on the regularized solution and examine parameter choice rules for finding the optimal regularization parameter for the assumed tolerance value. In addition, we discuss the prospect of reconstructing sparse solutions when tolerances are incorporated in the regularization functional.
