A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind
A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind
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DOI：
10.1080/00207160.2013.818137
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发表时间：
2014-05
影响因子：
1.8
通讯作者：
F. Lin;Shifeng Yang
中科院分区：
文献类型：
--
作者：
F. Lin;Shifeng Yang
数学和工程中的许多问题都会导致第一类Fredholm积分方程，例如信号和图像处理。这类方程是很难解决的数值，因为它们是不适定的。因此，需要正则化以获得合理的近似解。本文提出了一种新的基于加权H1算子的正则化方法。数值实现的细节。数值例子，包括一维和二维积分方程，来说明所提出的方法的效率。数值结果表明，该正则化方法可以恢复边缘和细节。
Many problems in mathematics and engineering lead to Fredholm integral equations of the first kind, e.g. signal and image processing. These kinds of equations are difficult to solve numerically since they are ill-posed. Therefore, regularization is required to obtain a reasonable approximate solution. This paper presents a new regularization method based on a weighted H1 seminorm. Details of numerical implementation are given. Numerical examples, including one-dimensional and two-dimensional integral equations, are presented to illustrate the efficiency of the proposed approach. Numerical results show that the proposed regularization method can restore edges as well as details.