两维信号最大信息量估计对偶极小化迭代算法(英文)

Algorithm for Two-dimensional Maximum Entropy Spectrum Estimation

在先人的工作中,由Burg首创的强信号谱估计的最大信息量方法,由于它的高分辨率特性,已证明是一种谱分析的有效技术。在一份尚未发表的报告中,Burg提出了两维形式的最大信息量估计问题。J.H.Me Clellan等人描述了多维ME谱估计一般解的方法。然而,两维ME问题则是极非线性的,至今还没有获得它的闭式解。由Lim和Malik所研究的解决这一问题的算法是一种迭代“交错射影”型的算法。本文提出了一种两维最大信息量估计的新方法,给出了ME问题的非线性规划与对偶非线性规划的结果,因而,两维ME的解可由两维对偶优化问题的解所获得。这一理论可推广到多维信号“相关匹配”ME问题。

In previous works, maximum entropy method of power spectral estimation, originally uggested by Burg, has proven to be a powerful teehnigue for spectral analysis, primarily due o ts high resolution properties. The form of two—dimensional maximum entropy spectral stimation roblem was solved by Burg in a unpublished report. The solution to general multi—dimensional aximum entropy spectral estimation was solved by J.H. MeClellan, et al. The two—dimensional aximum entropy problem, however, is highly nonlinear, and so far no any closed—form solution as yet been found. The algorithm researched by Lim and Malik to solve this problem is niterative 'alternating projections' type of algorithm. In this paper, the author will present ew method for maximum entropy spectrum estimation with two—dimensional signal. The result of onlinear programming for the maximum entropy with two—dimensional signal problem and a ualistic nonlinear programming will have been found。Then, maximum entropy spectrum estimation ith two—dimensional may be obtained as the solution to a two—dimensional dual optimization roblem. The theory is also extended to a 'correlation—matching' maximum entropy spectrum stimation with multi—dimensional signal。