Applications of the reproducing kernel theory to inverse problems and their engineering approach

结合核再现理论，提出了一种新的Thihonov正则化方法。使用我们的正则化方法，我们挑战了一些著名的和历史上困难的逆问题。此外，我们还设计了具体的算法来解决这些问题。重点研究了拉普拉斯变换的实逆变换、奇异值分解的求解方法、非线性映射的逆变换表示和混合信号的分离。此外，我们还为该领域的工程师申请了拉普拉斯变换反演算法的专利。

We developed a new type of Thihonov regularization combined with the theory of reproducing kernels. Using our method of regularization we have challenged some famous and historically difficult inverse problems. Furthermore we designed concrete algorithms for solving those problems. In particular we studied real inversion of Laplace transform, solving method by singular value decomposition, representation of inverse transform of nonlinear mapping and separation of mixed signals. In addition for engineer in the field we filed a patent application of our algorithm for inversion of Laplace transform.