Tikhonov regularization involves minimizing the combination of a data discrepancy term and a regularizing term, and is the standard approach for solving inverse problems. The use of non-convex regularizers, such as those defined by trained neural networks, has been shown to be effective in many cases. However, finding global minimizers in non-convex situations can be challenging, making existing theory inapplicable. A recent development in regularization theory relaxes this requirement by providing convergence based on critical points instead of strict minimizers. This paper investigates convergence rates for the regularization with critical points using Bregman distances. Furthermore, we show that when implementing near-minimization through an iterative algorithm, a finite number of iterations is sufficient without affecting convergence rates.

翻译：Tikhonov的正规化意味着将数据差异术语和常规化术语的结合最小化,这是解决反向问题的标准方法。使用非康韦克斯的正规化者,例如由受过训练的神经网络定义的常规化者,在许多情况下证明是有效的。然而,在非康维克斯情况下发现全球最低程度者可能具有挑战性,使现有的理论无法适用。最近在正规化理论方面的发展通过提供基于临界点的趋同而不是严格的最小化者而放松了这一要求。本文件调查使用布雷格曼距离的临界点实现正规化的趋同率。此外,我们表明,在通过迭接算法实施接近最小化时,一定数量的迭代法并不影响趋同率,就足够了。