论文标题
一种新型的两点梯度方法，用于正规化Banach空间中的反问题
A novel two-point gradient method for Regularization of inverse problems in Banach spaces
论文作者
论文摘要
在本文中，我们介绍了一种新型的两点梯度方法，用于解决Banach空间中的不足问题并研究其收敛分析。该方法基于众所周知的迭代正规陆地迭代方法以及推断策略。 BANACH空间中迭代正规化的陆网迭代方法的一般表述不包括某些功能的使用，例如惩罚功能，$ l^1 $功能等总变化等。本文中提出的新颖方案允许使用这些非平滑惩罚术语，这些刑罚术语可以在涉及涉及几个重要的解决方案的实际功能（例如零工）的实际应用中有用，例如涉及零用的组成率和分散的组成率。我们仔细讨论了重要参数的选择，例如该方法设计中涉及的组合参数和台阶大小。此外，我们讨论了一个示例来验证我们的假设。
In this paper, we introduce a novel two-point gradient method for solving the ill-posed problems in Banach spaces and study its convergence analysis. The method is based on the well known iteratively regularized Landweber iteration method together with an extrapolation strategy. The general formulation of iteratively regularized Landweber iteration method in Banach spaces excludes the use of certain functions such as total variation like penalty functionals, $L^1$ functions etc. The novel scheme presented in this paper allows to use such non-smooth penalty terms that can be helpful in practical applications involving the reconstruction of several important features of solutions such as piecewise constancy and sparsity. We carefully discuss the choices for important parameters, such as combination parameters and step sizes involved in the design of the method. Additionally, we discuss an example to validate our assumptions.
