卷积型方程的代数正则化解法及其在信号重建中的应用

Algebraic regularized method for solving the integral equation of convolution type with application to signal reconstruction

本文基于 Tikhonov的正则化思想 ,讨论了采用代数正则化方法数值求解卷积型方程的有关理论和技术问题 (包括离散正则解的存在唯一性 ,收敛性及数值稳定性等 ) ,并给出了在带限信号重建中的两个应用实例。理论分析和数值实验表明 :该算法具有很好的数值稳定性。

Base on Tikhonov's Regularized idea,some related problems of theory and techniques for solving the integral equation of convolution type by using algebraic regularized method is discussed in this paper.After the completion proof of existence,uniqueness and numerical stability of the described regularization solution,two applications to the signal reconstruction are also given.The theoretic analysis and numerical test indicate that the algorithm is well stabile numerical.