A new extrapolation algorithm for band-limited signals using the regularization method

The ill-posedness of the extrapolation problem in the presence of noise is considered. A stable algorithm is constructed by solving a Fredholm equation based on a regularization method. The algorithm appears relatively robust, since the noise eta /sub delta /(t) is taken as a function in L/sup 2/(-T,T)(T>0) such that the error energy integral mod eta /sub delta /(t) mod /sup 2/dt >

[1]  K. Senne,et al.  Performance advantage of complex LMS for controlling narrow-band adaptive arrays , 1981 .

[2]  Heinz-Josef Schlebusch,et al.  On a conjecture of J. L. C. Sanz and T. S. Huang , 1985, IEEE Trans. Acoust. Speech Signal Process..

[3]  Gonzalo R. Arce,et al.  Piecewise linear autoregressions through threshold decomposition , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[4]  J.-N. Lin,et al.  Adaptive nonlinear digital filter with canonical piecewise-linear structure , 1990 .

[5]  Gonzalo R. Arce Microstatistics in signal decomposition and the optimal filtering problem , 1992, IEEE Trans. Signal Process..

[6]  J. Cadzow,et al.  An extrapolation procedure for band-limited signals , 1979 .

[7]  Christodoulos Chamzas,et al.  On the extrapolation of band-limited functions with energy constraints , 1983 .

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

[9]  L. Onural,et al.  Median filtering by a generalized threshold decomposition , 1989 .

[10]  Ricardo H. Nochetto A stable extrapolation method for multidimensional degenerate parabolic problems , 1989 .

[11]  S. Thomas Alexander,et al.  Adaptive Signal Processing , 1986, Texts and Monographs in Computer Science.

[12]  Gonzalo R. Arce,et al.  Q-L transformations for adaptive generalized order statistic filtering , 1992, [Proceedings 1992] IEEE International Conference on Systems Engineering.

[13]  Edward J. Coyle,et al.  Minimum mean absolute error estimation over the class of generalized stack filters , 1990, IEEE Trans. Acoust. Speech Signal Process..

[14]  K. Nakayama A band-limited signal extrapolation algorithm using pseudo inverse filtering and heuristic optimization , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[15]  Junji Maeda,et al.  Restoration of band-limited images by an iterative regularized pseudoinverse method , 1984 .

[16]  H. Tsuji,et al.  Simultaneous optimization method of regularization and singular value decomposition in least squares parameter identification , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

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

[18]  Christodoulos Chamzas,et al.  An improved version of Papoulis-Gerchberg algorithm on band-limited extrapolation , 1984 .

[19]  X Ia ON A CONJECTURE OF BAND-LIMITED SIGNAL EXTRAPOLATION , 1986 .

[20]  R.W. Schafer,et al.  Constrained iterative restoration algorithms , 1981, Proceedings of the IEEE.

[21]  W. K. Jenkins,et al.  The use of orthogonal transforms for improving performance of adaptive filters , 1989 .

[22]  A. Jain,et al.  Extrapolation algorithms for discrete signals with application in spectral estimation , 1981 .

[23]  J. Sanz,et al.  Some aspects of band-limited signal extrapolation: Models, discrete approximations, and noise , 1983 .

[24]  R. Mersereau,et al.  Optimal estimation of the regularization parameter and stabilizing functional for regularized image restoration , 1990 .

[25]  Dante C. Youla,et al.  Generalized Image Restoration by the Method of Alternating Orthogonal Projections , 1978 .

[26]  J. Fitch,et al.  Median filtering by threshold decomposition , 1984 .

[27]  Neil J. Bershad On the optimum gain parameter in LMS adaptation , 1987, IEEE Trans. Acoust. Speech Signal Process..

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

[29]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[30]  朝倉 利光 R. B. Blackman and J. W. Tukey: The Measurement of Power Spectra, Dover Publications, Inc., New York, 1958, 208頁, 13.5×16cm, $1.85 , 1964 .

[31]  Petros Maragos,et al.  Morphological filters-Part II: Their relations to median, order-statistic, and stack filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[32]  W. Steenaart,et al.  An approach to band-limited signal extrapolation: The extrapolation matrix , 1978 .

[33]  Peter M. Clarkson,et al.  A class of order statistic LMS algorithms , 1992, IEEE Trans. Signal Process..