A comparison of stochastic gradient and minimum entropy deconvolution algorithms

Abstract This paper examines the connection between a stochastic gradient method for deconvolution, originally formulated in the electrical engineering literature , and minimum entropy type (ME-type) deconvolution methods, now well known in geophysics. It is shown that Gray's favoured ME-type deconvolution algorithm has a direct stochastic gradient equivalent which differs from the method examined here only in the presence of the inverse autocovariance matrix in Gray's method. The two procedures can be made more alike if the stochastic gradient algorithm is used merely for phase estimation, and is preceded by standard whitening deconvolution. In any event, the stochastic gradient approach is deficient in two respects, namely the assumption of an independent and identically distributed (iid) input sequence, and knowledge of its first and second absolute moments, assumptions which might be reasonable in the setting of data transmission problems, but not for seismic reflection coefficient sequences.

[1]  Y. Sato,et al.  A Method of Self-Recovering Equalization for Multilevel Amplitude-Modulation Systems , 1975, IEEE Trans. Commun..

[2]  Douglas W. Oldenburg,et al.  Automatic phase correction of common-midpoint stacked data , 1987 .

[3]  S.S. Reddi.  A time-domain adaptive algorithm for rapid convergence , 1984, Proceedings of the IEEE.

[4]  Andrew T. Walden,et al.  An investigation of the spectral properties of primary reflection coefficients , 1985 .

[5]  D. Godard,et al.  Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems , 1980, IEEE Trans. Commun..

[6]  M. Goursat.  Numerical results of stochastic gradient techniques for deconvolution in seismology , 1984 .

[7]  A. T. Walden,et al.  CORRECTING FOR COLOURED PRIMARY REFLECTIVITY IN DECONVOLUTION1 , 1988 .

[8]  A. Benveniste,et al.  Robust identification of a nonminimum phase system: Blind adjustment of a linear equalizer in data communications , 1980 .

[9]  Yakov Z. Tsypkin,et al.  Robust identification , 1980, Autom..

[10]  C. L. Mallows,et al.  Linear processes are nearly Gaussian , 1967 .

[11]  A. Walden.  Non-Gaussian reflectivity, entropy, and deconvolution , 1985 .

[12]  A. T. Walden,et al.  The nature of the non-Gaussianity of primary reflection coefficients and its significance for deconvolution , 1986 .

[13]  A. Walden,et al.  PRINCIPLES AND APPLICATION OF MAXIMUM KURTOSIS PHASE ESTIMATION1 , 1988 .

[14]  L. J. Griffiths,et al.  Adaptive deconvolution; a new technique for processing time-varying seismic data , 1977 .

[15]  Eweda Eweda,et al.  Convergence analysis of self-adaptive equalizers , 1984, IEEE Trans. Inf. Theory.