论文标题
非局部Tikhonov正则化的来源条件
Source Conditions for non-quadratic Tikhonov Regularisation
论文作者
论文摘要
在本文中，我们考虑了凸出的tikhonov正则化，以解决希尔伯特空间上线性操作员方程的解决方案。我们表明，可以使用标准的分数条件，以根据布雷格曼距离得出收敛速率，假设正则化项或其凸偶联物的凸性属性更强。在二次正则化的特殊情况下，我们能够重现经典理论已知的Hölder类型收敛速率的整个范围。
In this paper we consider convex Tikhonov regularisation for the solution of linear operator equations on Hilbert spaces. We show that standard fractional source conditions can be employed in order to derive convergence rates in terms of the Bregman distance, assuming some stronger convexity properties of either the regularisation term or its convex conjugate. In the special case of quadratic regularisation, we are able to reproduce the whole range of Hölder type convergence rates known from classical theory.
