An Application of Source Inequalities for Convergence Rates of Tikhonov Regularization with a Non-differentiable Operator
An Application of Source Inequalities for Convergence Rates of Tikhonov Regularization with a Non-differentiable Operator
复制标题
源不等式在不可微算子吉洪诺夫正则化收敛率中的应用
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
M. Grasmair
中科院分区：
文献类型：
--
作者：
M. Grasmair
本文研究一类不适定非线性算子方程稳定解的Tikhonov正则化。我们考虑的算子是连续的、紧的，但无处可微的，它与用于图像分割的活动轮廓模型有关。然而，我们能够通过采用变分或源不等式的方法，在不同的光滑性假设下的真解的收敛速度。通过这种方法，我们可以证明关于范数的线性收敛。
In this paper we study Tikhonov regularization for the stable solution of an ill-posed non-linear operator equation. The operator we consider, which is related to an active contour model for image segmentation, is continuous, compact, but nowhere differentiable. Nevertheless we are able to derive convergence rates under different smoothness assumptions on the true solution by employing the method of variational or source inequalities. With this approach, we can prove up to linear convergence with respect to the norm.