Wavelet parameter and phase estimation using cumulant slices

A simple, closed-form expression relates one-dimensional output cumulant statistics with the parameters of a known-order moving-average wavelet. Based on this relationship the author obtains unique parameter and phase estimates of autoregressive moving-average seismic wavelets. The input reflectivity sequence is assumed to be non-Gaussian, independent, and identically distributed. The wavelet is not assumed to be minimum phase and is allowed to include all-pass factors. The seismogram is contaminated by additive-colored Gaussian noise. Simulations demonstrate that the algorithm works well for moderate-size data records with a relatively low signal-to-noise ratio. >

[1]  T.J. Ulrych,et al.  Phase estimation using the bispectrum , 1984, Proceedings of the IEEE.

[2]  J. Mendel,et al.  Cumulant based identification of multichannel moving-average models , 1989 .

[3]  D. Stone.  Wavelet estimation , 1984, Proceedings of the IEEE.

[4]  G.B. Giannakis,et al.  Cumulant-based order determination of non-Gaussian ARMA models , 1990, IEEE Trans. Acoust. Speech Signal Process..

[5]  Jerry M. Mendel,et al.  Identification of nonminimum phase systems using higher order statistics , 1989, IEEE Trans. Acoust. Speech Signal Process..

[6]  M. Rosenblatt,et al.  Deconvolution and Estimation of Transfer Function Phase and Coefficients for NonGaussian Linear Processes. , 1982 .

[7]  F. Gantmacher,et al.  Applications of the theory of matrices , 1960 .

[8]  Yujiro Inouye,et al.  Cumulant based parameter estimation of multichannel moving-average processes , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[9]  Georgios B. Giannakis,et al.  ARMA modeling and phase reconstruction of multidimensional non-Gaussian processes using cumulants , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[10]  G. Giannakis.  Cumulants: A powerful tool in signal processing , 1987, Proceedings of the IEEE.

[11]  Ananthram Swami,et al.  ON ESTIMATING NON-CAUSAL ARMA NON-GAUSSIAN PROCESSES , 1988 .

[12]  B. Friedlander,et al.  Optimal estimates of MA and ARMA parameters of non-Gaussian processes from high-order cumulants , 1988, Fourth Annual ASSP Workshop on Spectrum Estimation and Modeling.

[13]  M.R. Raghuveer,et al.  Bispectrum estimation: A digital signal processing framework , 1987, Proceedings of the IEEE.

[14]  Jitendra K. Tugnait,et al.  On selection of maximum cumulant lags for noncausal autoregressive model fitting , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[15]  Chrysostomos L. Nikias,et al.  Bispectrum estimation: A parametric approach , 1985, IEEE Trans. Acoust. Speech Signal Process..