This paper is concerned with an inverse scattering problem in frequency domain, when the scattered field is governed by the Helmholtz equation. The algorithm is iterative in nature. It introduces a new approach which we refer to as proper solution space. It assumes an initial guess for the unknown function and obtains corrections to the guessed value. The updating stage is accomplished by generating a set of functions that satisfy some of the required boundary conditions. We refer to this space as proper solution space. The correction to the assumed value can then be obtained by imposing the remaining boundary conditions. A number of numerical examples are used to study the applicability and effectiveness of the new approach.

中文翻译：

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基于适当解空间的逆散射

当散射场由亥姆霍兹方程控制时，本文关注频域中的逆散射问题。该算法本质上是迭代的。它引入了一种新方法，我们称之为适当的解决方案空间。它假设未知函数的初始猜测并获得对猜测值的修正。更新阶段是通过生成一组满足某些所需边界条件的函数来完成的。我们将此空间称为适当的解决方案空间。然后可以通过施加剩余的边界条件来获得对假设值的校正。许多数值例子被用来研究新方法的适用性和有效性。