A weighted H~1 seminorm regularization method for Fredholm integral equations of the first kind

摘要

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 H~1 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.