Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative regularization methods. Superiorization is a heuristic approach that can steer basic iterative algorithms to have small value of certain regularization functional while keeping the algorithms simplicity and computational efforts, but is able to account for additional prior information. In this note, we combine the superiorization methodology with iterative regularization methods and show that the superiorized version of the scheme yields again a regularization method, however accounting for different prior information.

翻译：逆问题因其固有的非唯一性和对数据扰动的敏感性而具有显著特征。其稳定求解需要应用包括变分正则化与迭代正则化在内的正则化方法。改进是一种启发式方法，能够在保持基础迭代算法简洁性与计算效率的同时，通过引导算法获得特定正则化泛函的最小值，从而整合额外的先验信息。本文结合改进方法论与迭代正则化方法，论证该方案的改进版本仍能构成一种正则化方法，并进一步整合了不同的先验信息。