Signal reconstruction from the phase of the bispectrum

The authors present a simple procedure, the bispectrum signal reconstruction (BSR) algorithm, to recover the Fourier phase of a signal from the phase of its bispectrum. By simple analogy, a procedure that recovers the Fourier magnitude of a signal from the magnitude of its bispectrum is also presented. In addition, the authors propose an iterative scheme, the bicepstrum iterative reconstruction algorithm (BIRA), for the reconstruction of a finite impulse response (FIR) sequence from only the phase of its bispectrum, and they demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm. Both schemes are based on the key observation that the differences of the bispectrum coefficients contain all the information concerning the Fourier phase of the signal, whereas their sums contain the Fourier-magnitude information. >

[1]  M. Hayes,et al.  Convergence of iterative nonexpansive signal reconstruction algorithms , 1981 .

[2]  A. Oppenheim,et al.  Iterative techniques for minimum phase signal reconstruction from phase or magnitude , 1980 .

[3]  Henry Stark,et al.  Image recovery: Theory and application , 1987 .

[4]  R. Gerchberg.  Super-resolution through Error Energy Reduction , 1974 .

[5]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[6]  G. Giannakis,et al.  FIR modeling using log-bispectra: weighted least-squares algorithms and performance analysis , 1991 .

[7]  D. Youla,et al.  Image Restoration by the Method of Convex Projections: Part 1ߞTheory , 1982, IEEE Transactions on Medical Imaging.

[8]  J R Fienup,et al.  Reconstruction of an object from the modulus of its Fourier transform. , 1978, Optics letters.

[9]  Chrysostomos L. Nikias,et al.  Bicepstrum computation based on second- and third-order statistics with applications , 1990, International Conference on Acoustics, Speech, and Signal Processing.

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

[11]  A.V. Oppenheim,et al.  The importance of phase in signals , 1980, Proceedings of the IEEE.

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

[13]  Saleh A. Alshebeili,et al.  A phase reconstruction algorithm from bispectrum (seismic reflection data) , 1990 .

[14]  Ahmet Enis Cetin,et al.  An algorithm for signal reconstruction from bispectrum , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[15]  Chrysostomos L. Nikias,et al.  Blind deconvolution based on signal reconstruction from partial information using higher-order spectra , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[16]  Raghuveer M. Rao,et al.  Bispectral reconstruction of signals in noise: amplitude reconstruction issues , 1990, IEEE Trans. Acoust. Speech Signal Process..

[17]  A. Oppenheim,et al.  Signal reconstruction from phase or magnitude , 1980 .

[18]  Chrysostomos L. Nikias,et al.  Phase reconstruction in the trispectrum domain , 1987, IEEE Trans. Acoust. Speech Signal Process..

[19]  A. Papoulis.  A new algorithm in spectral analysis and band-limited extrapolation. , 1975 .

[20]  Monson H. Hayes,et al.  Iterative Procedures For Signal Reconstruction From Phase , 1980, Other Conferences.

[21]  Saleh Alshebeili,et al.  A Phase Reconstruction Algorithm From Bispectrum , 1990 .

[22]  M. Sezan,et al.  Image Restoration by the Method of Convex Projections: Part 2-Applications and Numerical Results , 1982, IEEE Transactions on Medical Imaging.