Predictive Deconvolution: (Part 1)

REFERENCES

• P.S. Moharir, Deconvolution by cepstral transformation, Journal of IETE, vol 28, pp 515–532, Oct 1982.
   Google Scholar
• W.H. Bakun & L.R. Johnson, The deconvolution of teleseismic P waves from explosions: Milrow and Cannikin, Geophys. J Roy Astr Soc, vol 34, pp 321–342, Nov 1973.
   Web of Science ®Google Scholar
• D.G. Childers, D.P. Skinner & R.C. Kemerait, The cepstrum: a guide to processing, Proc IEEE, vol 65, pp 1428–1443, Oct 1977.
   Web of Science ®Google Scholar
• J.S. Kim, Spectral root homomorphic deconvolution system, IEEE Trans, vol ASSP-27, pp 223–233, Jun 1979.
   Google Scholar
• A.V. Oppenheim (Ed), Applications of digital signal processing, Prentice-Hall, Englewood Cliffs, 1978, pp 140–162.
   Google Scholar
• T.F. Quatieri Jr., Minimum and mixed phase speech analysis-synthesis by adaptive homomorphic deconvolution, IEEE Trans, vol ASSP-27, pp 328–335, Aug 1979.
   Google Scholar
• T.V. Ananthapadmanabha, Composite signal deconvolution by digital inverse filtering, ibid., vol ASSP-27, pp 95–97, Feb 1979.
   Google Scholar
• T.V. Ananthapadmanabha & B. Yegnanarayana, Epoch extraction from linear prediction residual for identification of closed glottis intervals, ibid., vol ASSP-27, pp 309–319, Aug 1979.
   Google Scholar
• B.S. Atal & S.L. Hanauer, Speech analysis and synthesis by linear prediction of the speech wave, J. Acoust. Soc. Am, vol 50, pp 637–655, Feb 1971.
   PubMed Web of Science ®Google Scholar
• A.J. Berkhout, Least-squares inverse filtering and wavelet deconvolution, Geophysics, vol 42, pp 1369–1383, Jul 1977.
   Web of Science ®Google Scholar
• A.J. Barkhout & P.R. Zaanen, A comparison between Wiener filtering, Kalman filtering, and deterministic least squares estimation, Geophys Prospect, vol 24, pp 141–197, Mar 1976.
   Google Scholar
• P. Bois, Autoregressive pattern recognition applied to the delimitation of oil and gas reservoirs, ibid., vol 28, pp 572–591, Aug 1980.
   Google Scholar
• W.R. Burns, A Statistically optimized deconvolution, Geophysics, vol 33, pp 255–263, Apr 1968.
   Web of Science ®Google Scholar
• J.F. Claerbout & E.A. Robinson, A short note on the error in least squares inverse filtering, ibid., vol 29, pp 118–120, Feb 1964.
   Google Scholar
• G.A. Clark & P.W. Rodgers, Adaptive prediction applied to seismic event detection, Proc IEEE, vol 69, pp 1166–1168, Sept 1981.
   Web of Science ®Google Scholar
• G.K.C. Clarke, Time-varying deconvolution filters, Gcophysics, vol 33, pp 936–944, Dec 1968.
   Web of Science ®Google Scholar
• N.D. Crump, A Kalman filter approach to the deconvolution of seismic signals, ibid., vol 39, pp 1–13, Feb 1974.
   Google Scholar
• E.B. Davies & E.J. Mercado, Multichannel deconvolution filtering of field recorded seismic data, ibid., vol 33, pp 711–722, Oct 1968.
   Google Scholar
• G.J. Fryer, M.E. Odegard & G.H. Sutton, Deconvolution and spectral estimation using final prediction error, ibid., vol 40, pp 411–425, Jun 1975.
   Google Scholar
• L.J. Griffiths, F.R. Smolka & L.D. Trembly, Adaptive deconvolution—a new technique for processing time-vayring seismic data, ibid., vol 42, pp 742–759, Jun 1977.
   Google Scholar
• B.J. Mitchell, M. Landisman & Z.A. Der, Predictive deconvolution applied to long range seismic refraction observations, Pure and App. Geophys., vol 96, pp 127–133, IV, 1972.
   Web of Science ®Google Scholar
• K.L. Peacock & S. Tretiel, Predictive deconvolution-theory and practice, Geophysics, vol 34, pp 155–169, Apr 1969.
   Web of Science ®Google Scholar
• R.B. Rice, Inverse deconvolution filters, ibid., vol 27, pp 4–18, Feb 1962.
   Google Scholar
• E.A. Robinson, Predictive decomposition of time-series with applications to seismic exploration, MIT Cambridge, PhD thesis, 252 pp, 1954. Also Geophysics, vol 32, pp 418–484, Jun 1967.
   Google Scholar
• E.A. Robinson, Predictive deconvolution of seismic traces, Geophysics, vol 22, pp 767–778, Dec 1957.
   Google Scholar
• E.A. Robinson, Statistical communication and detection, Hafner, New York, 1967.
   Google Scholar
• E.A. Robinson, Dynamic predictive deconvolution, Geophys Prospect, vol 23, pp 780–798, Dec 1975, Comments by V. Bardan, vol 25, pp 569–572, Sept 1977, Reply by author, vol 25, p 572, Sept 1977.
   Google Scholar
• E.A. Robinson & S. Treitel, Principles of digital Wiener filtering, Geophys Prospect, vol 15, pp 311–333, Sept 1967.
   Google Scholar
• M.T. Silvia & E.A. Robinson, Deconvolution of geophysical time-series in the exploration for oil and natural gas, Elsevier, Amsterdam, 1979, 251 pp.
   Google Scholar
• J.B. Sinton, R.W. Ward & J.S. Watkins, Suppression of long-delay multiple reflections by predictive deconvolution, Geophysics, vol 43, pp 1352–1367, Dec 1978.
   Web of Science ®Google Scholar
• H.L. Taylor, S.C. Banks & J.F. McCoy, Deconvolution with L-one norm, Geophysics, vol 44, pp 39–52, Jan 1979.
   Web of Science ®Google Scholar
• R.J. Wang, Adaptive predictive deconvolution of seismic data, Geophys Prospect, vol 25, pp 342–381, Jun 1977.
   Google Scholar
• S.M. Deregowski, Self-matching deconvolution in the frequency domain, ibid., vol 26, pp 252–290, Mar 1978.
   Google Scholar
• M.R. Foster, R.L. Sengbush & R.J. Watson, Use of Monte Carlo techniques in optimum design of the deconvolution process, Geophysics, vol 33, pp 945–949, Dec 1968.
   Web of Science ®Google Scholar
• D.D. Jackson, The use of a priori data to resolve non-uniqueness in linear inversion, Geophys, J Roy Astr Soc, vol 57, pp 137–157, Apr 1979.
   Web of Science ®Google Scholar
• G.E. Kopec, A.V. Oppenheim & J. M. Tribolet. Speech analysis by homomorphic prediction, IEEE Trans, vol ASSP-25, pp 40–49, Feb 1977.
   Google Scholar
• G. Kunetz & J.M. Fourmann, Efficient deconvolution of marine seismic records, Geophysics vol 33, pp 412–423, Jun 1968.
   Web of Science ®Google Scholar
• L.J.B. La Coste, Deconvolution by successive approximations, ibid., vol 47, pp 1724–1730, Dec 1982.
   Google Scholar
• L.R. Lines & T.J. Ulrych, The old and the new in seismic deconvolution and wavelet estimation, Geophys Prospect, vol 25, pp 512–540, Sept 1977, Correction in vol 26, p 293, Mar 1978.
   Google Scholar
• N.S. Neidell, Short note-deterministic deconvolution operators—3 point or 4 point, Geophysics, vol 37, pp 1039–1042, Dec 1972.
   Web of Science ®Google Scholar
• J.M. Mendel & J. Kormylo, Single-channel white-noise estimators for deconvolution, Geophysics, vol 43, pp 102–124, Feb 1978.
   Web of Science ®Google Scholar
• D.W. Oldenburg, A comprehensive solution to the linear deconvolution problem, Geophys. J Roy Astr Soc, vol 65, pp 331–357. May 1981.
   Web of Science ®Google Scholar
• A V. Oppenheim, G.E. Kopec & J.M. Tribolet, Signal analysis by homomorphic prediction, IEEE Trans, vol ASSP-24, pp 327–332, Aug 1976.
   Google Scholar
• T.K. Sarkar, D.D. Weiner, V.K, Jain & S.A. Dianat, Impulse response determination in the time domain theory, ibid., vol AP-30, pp 657–663, Jul 1982.
   Google Scholar
• P.C. Sabatier, Comments on “The use of a priori data to resolve nonuniqueness in linear inversions” by D.D. Jackson, Geophys, J Roy Astr Soc, vol 58, pp 523–524, Aug 1979.
   Google Scholar
• H.F. Silverman & A.E, Pearson, On deconvolution using the discrete Fourier transforms IEEE Trans, vol AU-21, pp 112–118, Apr 1973.
   Google Scholar
• S. Treitel & E.A. Robinson, Deconvolution-homorrorphic o predictive? IEEE Trans, vol GE-15, pp 11–13, Jan 1977.
   Google Scholar
• A. Ziolkowski, Further thoughts on Popperian geophysics—the example of deconvolution, Geophys Prospect, vol 30 pp 155–165, Apr 1982.
   Web of Science ®Google Scholar
• A.M. Ziolkowski, W.E. Lerwill, D.W. March & L.G. Peardon, Wavelet deconvolution using a source scaling law, Geophys. Prospect, vol 28, pp 872–901, Dec 1980.
   Web of Science ®Google Scholar
• A Kolmogorov, Interpolation und extrapolation von Stationaren zufalligen folgen, Bull Acad Sci USSR Ser Math, vol 5, pp 3–14, 1941.
   Google Scholar
• N. Wiener, Extrapolation, interpolation and smoothing of stationary time series with engineering applications, MIT Press, Cambridge, Mass, 1949, pp 163.
   Google Scholar
• J.E. Abate, Linear and adaptive delta modulation, Proc IEEE, vol 55, pp 298–308, Mar 1967.
   Web of Science ®Google Scholar
• B.S. Atal & M.R. Schroder, Adaptive predictive coding of speech signals, Bell Syst Tech J, vol 49, pp 1968–1973, Oct 1970.
   Google Scholar
• A.H. Haddad & J.V. Bodycomb, Some properties of a predictive quantizing system, IEEE Trans, vol COM-18, pp 682–684, Oct 1970.
   Google Scholar
• D.J. Connor, R.F.W. Pease & W.G. Scholes, Television coding using two dimensional spatial prediction, Bell Syst Tech J, vol 50, pp 1049–1063, Mar 1971.
   Google Scholar
• J.G. Dunn, An experimental 9600-bits/s voice digitizer employing adaptive prediction, IEEE Trans, vol COM-19, pp 1021–1032, Dec 1971.
   Google Scholar
• P. Elias, Predictive coding, IRE Trans, vol 1T-1, pp 16–33, Mar 1955.
   Web of Science ®Google Scholar
• J.D. Gibson, Sequentially adaptive backward prediction in ADPCM speech coders, IEEE Trans, vol COM-26, pp 145–150, Jan 1978.
   Google Scholar
• J.D. Gibson, Adaptive prediction in speech differential encoding systems, Proc IEEE, vol 68, pp 488–525, Apr 1980.
   Web of Science ®Google Scholar
• R.E. Kalman, A new approach to linear filtering and prediction problems, J Basic Engg, vol 82, pp 342–345, Mar 1960.
   Google Scholar
• R. Lippmann, A technique for channel error correction in differential PCM picture transmission, IEEE Internat Conf on Communication, vol 11, pp 48–12 to 48–18, Jun 11–13, 1973.
   Google Scholar
• J. Makhoul, Spectral analysis of speech by linear prediction, IEEE Trans, vol AU-21, pp 140–148, Jun 1973.
   Google Scholar
• J. Makhoul, Linear prediction: a tutorial review, Proc IEEE, vol 63, pp 561–580, Apr 1975.
   Web of Science ®Google Scholar
• J. Makhoul, Spectral linear prediction: properties and applications, IEEE Trans, vol ASSP-23, pp 283–296, Jun 1975.
   Google Scholar
• J. Makhoul & M. Berouti, Adaptive noise spectral shaping and entropy coding in predictive coding of speech, ibid., vol ASSP-27, pp 63–73, Feb 1979.
   Google Scholar
• R.A. Mc Donald, Signal-to-noise and idle channel performance of differential pulse code modulation systems-particular applications to voice signals, Bell Syst Tech J, vol 45, pp 1123–1151, Sept 1966.
   Google Scholar
• H.G. Musmann, A comparison of extended differential coding schemes for video signals, Proc IEEE Internat Seminar on Digital Communication, Zurich, 1974, pp CI (1)–C1(7).
   Google Scholar
• B.M. Oliver, Efficient coding, Bell Syst Tech J, vol 31, pp 776–786, July 1952.
   Google Scholar
• J.B. O'Neal Jr. & R.W. Stroh, Differential PCM for speech and data signals, IEEE Trans, vol COM-20, pp 900–912, Oct 1972.
   Google Scholar
• L.A. Shepp, D. Slepian & A.D. Wyner, On prediction of moving average processes, Bell Syst Tech J, vol 59, pp 367–415, Mar 1980.
   Google Scholar
• J.A. Cadzow, An extrapolation procedure for bandlimited signals, IEEE Trans, vol ASSP-27, pp 4–12, Feb 1979.
   Google Scholar
• A. Papoulis, A new algorithm in spectral analysis and band-limited extrapolation, IEEE Trans, vol CAS-22, pp 735–742, Sept 1975.
   Google Scholar
• M.S. Sabri & W. Steenaart, An approach to band-limited signal extrapolation: the extrapolation matrix, IEEE Trans, vol CAS-25, pp 74–78, Feb 1978.
   Google Scholar
• M.S. Sabri & W. Steenaart, Comments on “An extrapolation procedure for band-limited signals” IEEE Trans, vol ASSP-28, p 254, Apr 1980.
   Google Scholar
• P.S. Moharir, Band-limited signals. Students' J Inst Electron & Telecomin Engrs, vol 21, pp 13–18, Jan 1980.
   Google Scholar
• A. Papoulis, Signal analysis, McGraw-Hill, New York, 1977, pp 431.
   Google Scholar
• D. Slepian, On bandwidth, Proc IEEE, vol 64, pp 292–300, Mar 1976.
   Web of Science ®Google Scholar
• G.J. Bluck, Radar mapping: prolate spheroidal wave functions versus truncated inverse Fourier transform, IEEE Trans, vol AP-20, pp 188–193, Mar 1972.
   Google Scholar
• H.J. Landau, H.O. Pollak & D. Slepian, Prolate spheroidal wave functions, Parts I, II, III, Bell Syst Tech J, vol 40, pp 43–64, 65–84, Jan 1961, vol 41, pp 1295–1336, Jul 1962.
   Google Scholar
• D. Slepian, Prolate spheroidal wave functions, Fourier analysis and uncertainty, Part IV, V, Bell Syst Tech J, vol 43, pp 3009–3058, Nov 1964, vol 57, pp 1371–1430, May-Jun 1978.
   Google Scholar
• D.E. Vakman, Sophisticated signals and the uncertainty principle in radar, Ed. E. Jacobs, Springer-Verlag, Berlin, 1968 pp 240–243.
   Google Scholar
• H. Akaike, Fitting autoregressive models for prediction, Ann Inst Statist, vol 21, pp 243–247, 1969.
   Web of Science ®Google Scholar
• S. Bruzzone & M. Kaveh, On some suboptimum ARMA spectral estimators, IEEE Trans, vol ASSP-28, pp 753–755, Dec 1980.
   Google Scholar
• J.A. Cadzow, High performance spectral estimation—a new ARMA method, ibid., vol ASSP-28, pp 524–592, Oct 1980.
   Google Scholar
• J. Durbin, Efficient estimation of parameters, in moving average models, Biometrika, vol 46, pp 306–316, 1959.
   Web of Science ®Google Scholar
• J. Durbin, The fitting of time series models, Rev Inst hit Statist, vol 28, pp 233–243, 1960.
   Google Scholar
• B. Friedlander, Lattice filters for adaptive processing, Proc IEEE, vol 70, pp 829–867, Aug 1982.
   Web of Science ®Google Scholar
• W. Gersch & D.R. Sharpe, Estimation of power spectra with finite order autoregressive models, IEEE Trans, vol AC-18, pp 367–369, Aug 1973.
   Google Scholar
• L.J. Griffiths & R. Prieto-Diaz, Spectral analysis of natural seismic events using autoregressive techniques, IEEE Trans. vol GE-15, pp 13–25, Jan 1977.
   Google Scholar
• S.M. Kay, Noise compensation for autoregressive spectral estimates, IEEE Trans, vol ASSP-28, pp 292–303, Jun 1980.
   Google Scholar
• S.M. Kay, A new ARMA spectral estimator, IEEE Trans, vol ASSP-28. pp 585–588, Oct 1980.
   Google Scholar
• D.T.L. Lee, B. Friedlander & M. Morf. Recursive ladder algorithms for ARMA modelling, IEEE Trans, vol AC-27, pp 753–764, Aug 1982.
   Google Scholar
• L. Marple, A new autoregressive spectrum analysis algorithm, IEEE Trans, vol ASSP-28, pp 441–454, Aug 1980.
   Google Scholar
• A.S, Poznyak, Estimating the parameters of autoregressive process by the method of least squares, Int J Syst Sci, vol 11 pp 577–588, May 1980.
   Web of Science ®Google Scholar
• T.J. Ulrych & T. Bishop. Maximum entropy spectral analysis and autoregressive decomposition, Rev Geophysics, vol 13, pp 183–200, Feb 1975.
   Web of Science ®Google Scholar
• T.J, Ulrych & R. W. Clayton, Time series modelling and maximum entropy, Phys Earth and Plan Inter, vol 12, pp 188–200, Aug 1976.
   Web of Science ®Google Scholar
• F, Yarman & B.W. Dickinson, Autoregressive estimation using final prediction error. Proc IEEE, vol 70, pp 872–873. Aug 1982.
   Web of Science ®Google Scholar
• U.G. Yule, On a method for investigating periodicities in distributed series with special reference to Wolfer's sunspot numbers, Phil Trans Roy Soc London, vol 226, pp 267–298, Ser A, 1927.
   Google Scholar
• T.W. Anderson, The statistical analysis of time series, John Wiley, New York, 1971.
   Google Scholar
• G.E, Box & G.M. Jenkins, Time-series analysis: forecasting and control, Holden-Day. San Francisco, 1976, 575 pp.
   Google Scholar
• E.J. Hannan, Time series analysis, Methuen, London, 1960.
   Google Scholar
• W. Rosenblatt (Ed), Time series analysis, John Wiley, New York, 1963.
   Google Scholar
• P. Whittle, Prediction and regulation by linear least-squares methods, English Universities Press, London, 1963.
   Google Scholar
• H. Wold, A study in the analysis of stationary time series, Almquist and Wiksell, Stockholm, 1954.
   Google Scholar
• J.W. Bayless & E.O. Brigham, Application of the Kalman filter, Geophysics, vol 35, pp 2–23, Feb 1970
   Web of Science ®Google Scholar
• H. W. Bode & C.E. Shannon, A simplified derivation of linear least squares smoothing and prediction theory, Proc IRE, vol 38, pp 417–425, Apr 1950.
   Google Scholar
• M.J. Grimble, Solution of the Kalman filtering problem for stationary noise and finite data records, Int J Syst Sci, vol 10, pp 117–196. Feb 1979.
   Google Scholar
• S.W. Lang & J.H. McClellan, A Simple proof of stability for all-pole linear prediction models, Proc IEEE, vol 67, pp 860–861, May 1979.
   Web of Science ®Google Scholar
• S.A. Tretter & K. Steiglitz, Power spectrum identification in terms of rational models, IEEE Trans, vol AC-12, pp 185–188, Apr 1967.
   Google Scholar
• Y.W. Lee, Statistical theory of communication, John Wiley, New York, 1966, pp 56–59, 93–96, 369–394.
   Google Scholar
• C.D. Green, Integral equation methods. Nelson, London, 1969, pp 81–114
   Google Scholar
• G. Hoheisel & R.M. Tropper, Integral equations, Nelson, London, 1967, pp 44–48.
   Google Scholar
• J.S. Meditch, Stochastic optimal linear estimation and control, McGraw-Hill, New York, 1969, p 164
   Google Scholar
• P.A. Bello, R.N. Lincoln & H. Gish. Statistical delta modulation, Proc IEEE, vol 55, pp 308–316, Mar 1967.
   Web of Science ®Google Scholar
• T. Fine, Properties of an optimum digital system and applications, IEEE Trans, vol IT-10. pp 287–296, Oct 1964.
   Google Scholar
• H. Akaike, Block Toeplitz matrix inversion, SIAM J Appl Math, vol 24, Mar 1973.
   Web of Science ®Google Scholar
• L.J. Derr, Inversion of isoclinal matrices, Math Compta, vol 26, pp 719–721, July 1972.
   Web of Science ®Google Scholar
• B.W. Dickinson, Efficient solution of linear equations with banded Toeplitz matrices, IEEE Trans, vol ASSP-27, pp 421–423, Aug 1979.
   Google Scholar
• R.M. Gray, On the asymptotic eigenvalue distribution of Toeplitz matrices, IEEE Trans, vol IT-18, pp 725–730, Nov 1972.
   Google Scholar
• U. Grerander & G. Szego, Toeplitz forms and their applications. University of California Press, Berkeley. 1958.
   Google Scholar
• R.P. Menz, On the inverse of some covariance matrices of Toeplitz type, SIAM J Appl Math, vol 31, pp 426–437, Nov 1976.
   Web of Science ®Google Scholar
• D.H. Preis, The Toeplitz matrix: its occurrence in antenna problems and a rapid inversion algorithm, IEEE Trans, vol AP-20, pp 204–206, Mar 1972.
   Google Scholar
• J. Rissanen, Algorithms for triangular decomposition of block Hankel and Toeplitz matrices with applications to factoring positive matrix polynomials. Math Comput, vol 27, pp 147–154, Jan 1973.
   Web of Science ®Google Scholar
• P.A. Roebuck & S. Barnett, A survey of Toeplitz and related matrices, Int J Syst Sci, vol 9, pp 921–934, Aug 1978.
   Web of Science ®Google Scholar
• W. F. Trench, An algorithm for the inversion or finite Toeplitz matrices, J Soc Indust Appl Math, vol 12, pp 515–522, Sept 1964.
   Google Scholar
• S. Zohar, Toeplitz matrix inversion: the algorithm of W.F. Trench, J Assoc Comput Math, vol 16, pp 592–601, Oct 1969.
   Web of Science ®Google Scholar
• S. Zohar, Fortran subroutines for the solution of Toeplitz sets of linear equations., IEEE Trans, vol ASSP-27, pp 656–658, Dec 1979.
   Google Scholar
• W.S. Dunbar, An in-place Levinson update algorithm, Proc IEEE, vol 69, pp 754–755, Jun 1981.
   Web of Science ®Google Scholar
• B. Friedlander, A recursive maximum likelihood algorithm for ARMA spectral estimation, IEEE Trans, vol IT-28, pp 639–646. July 1982.
   Google Scholar
• N. Levinson, The Wiener RMS (root-mean square) error criterion in filter design and prediction, J Math Phys, vol 25, pp 261–278, 1947, Also as Appendix B in Ref 51. pp 129–148.
   Web of Science ®Google Scholar
• J. Makhoul, Stable and efficient lattice methods for linear prediction, IEEE Trans, vol ASSP-25, pp 423–428, Oct 1977.
   Google Scholar
• M. Saito, Round off error in Levinson's algorithm for solving least-squares filters, Butsuri Tanko, vol 32, pp 7–13, 1979.
   Google Scholar