WAVELET-BASED ESTIMATOR FOR THE HURST PARAMETERS OF FRACTIONAL BROWNIAN SHEET  

作　　者：吴量 丁义明 

机构地区：[1]Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan 430071,China [2]University of Chinese Academy of Sciences,Beijing 100049,China [3]Department of Mathematics,Wuhan Institute of Technology,Wuhan 430070,China [4]Key Laboratory of Magnetic Resonance in Biological Systems,Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan 430071,China

出　　处：《Acta Mathematica Scientia》2017年第1期205-222,共18页数学物理学报（B辑英文版）

基　　金：supported in part by the National Basic Research Program of China(973 Program,2013CB910200,and 2011CB707802)

摘　　要：It is proposed a class of statistical estimators H = （H1,… ,Hd） for the Hurst parameters H = （H1,… ,Hd） of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are asymptotically normal. These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals, which is important in texture classification and improvement of diffusion tensor imaging （DTI） of nuclear magnetic resonance （NMR）. Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators. We find that when Hi ≥ 1/2, the estimators are accurate, and when Hi 〈 1/2, there are some bias.It is proposed a class of statistical estimators H = （H1,… ,Hd） for the Hurst parameters H = （H1,… ,Hd） of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are asymptotically normal. These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals, which is important in texture classification and improvement of diffusion tensor imaging （DTI） of nuclear magnetic resonance （NMR）. Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators. We find that when Hi ≥ 1/2, the estimators are accurate, and when Hi 〈 1/2, there are some bias.

关 键 词：detection of long-range dependence SELF-SIMILARITY Hurst parameters waveletanalysis fractional Brownian sheet 

分 类 号：O174.2[理学—数学]