文献类型：期刊文献

中文题名：带限信号重构问题的迭代正则化方法

英文题名：Iterative regularization method for reconstruction of band-limited signal

作者：马青华[1,2];许作良[1];李艳涛[2];闫俐[1]

第一作者：马青华

机构：[1]中国人民大学信息学院;[2]北京联合大学应用文理学院

第一机构：中国人民大学信息学院,北京100872

年份：2011

卷号：37

期号：6

起止页码：98-101

中文期刊名：兰州理工大学学报

外文期刊名：Journal of Lanzhou University of Technology

收录：CSTPCD;;北大核心:【北大核心2008】；

基金：国家自然科学基金(11171349);北京市优秀人才培养资助个人项目(2010D005022000008)

语种：中文

中文关键词：带限信号重构;正则化方法;最速下降法;预条件

外文关键词：band-limited signal reconstruction; regularization method; steepest descent method; precon-ditioning

摘要：针对带限信号重构问题的迭代正则化方法,提出用Landweber迭代法和最速下降法求解低频带限信号重构问题,导出正则化问题的预条件梯度迭代格式,并对三种方法进行比较,进行数值模拟的结果表明:最速下降法与Landweber迭代法具有非常相似的迭代公式,最速下降法既是正则化方法,又可以最优选取迭代步长,比Land-weber迭代法具有更快的收敛性,将预条件方法用到正则化问题上可以起到稳定和快速求解的作用.通过数值算例表明,在计算效率上预条件梯度迭代正则化方法优于Landweber迭代算法和传统的最速下降法.
Aimed at the iterative regularization methods for band-limited signal reconstruction, Land- weber iterative method and steepest descent method were presented for solving the low-frequency band- limited signal reconstruction problem. The preconditioning gradient iterative format was derived for regularization problem. Numerical simulations were also performed and compared for above-mentioned meth- ods. It was concluded that although the steepest descent method and Landweber iterative method had very similar iterative formula, the former was not only a regularization method but also could optimally choose the iterative step length, having faster convergency than the Landweber iterative method. By using the preconditioning technique for the regularization problem, the stability and fast solution could be obtained. It was shown by a numeric example that in connection of computational efficiency the preconditioning gra- dient descent method was better than the Landweber iterative method and the traditional steepest descent method.