A band-limited signal extrapolation algorithm using pseudo inverse filtering and heuristic optimization

A target-oriented strategy can be applied to estimate a wave-equation least-squares inverse (LSI) image. By explicitly computing the wave-equation Hessian, the LSI image is obtained as the solution of a nonstationary least-squares inverse filtering problem. The rows of the Hessian are the nonstationary filters containing information about the acquisition geometry, the velocity model, and the band-limited characteristics of the seismic data. By exploiting the sparsity and the structure of the Hessian matrix, a large number of iterations, necessary to achieve convergence, can be computed cheaply. The results on a structurally complex model show the improvements of the LSI image versus the migrated image.

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Performance and limitation of discrete band-limited signal extrapolation

10.1109/icassp.1986.1168932 ◽

2005 ◽

Cited By ~ 4

Author(s):

H. Lee ◽

Z. Lin ◽

T. Huang

Keyword(s):

Discrete Band ◽

Band Limited ◽

Signal Extrapolation

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Multichannel Structural Inverse Filtering

Journal of Vibration and Acoustics ◽

10.1115/1.3269147 ◽

1984 ◽

Vol 106 (1) ◽

pp. 22-28 ◽

Cited By ~ 16

Author(s):

R. E. Powell ◽

W. Seering

Keyword(s):

Response Functions ◽

Inverse Filtering ◽

Inverse Filter ◽

Vibration Measurements ◽

Input Force ◽

Multiple Input ◽

Time Histories ◽

Force Time ◽

Value Decomposition ◽

Pseudo Inverse

A technique has been implemented for predicting the multiple input force time histories acting on a machinery component through the use of multiple vibration measurements and a stored matrix of mechanical frequency response functions. A least squares pseudo-inverse of this transfer matrix is computed in the frequency domain using the singular value decomposition. This decomposition is used to condition the pseudo-inverse against potential singularities caused by uncertainties in the data. The constructed inverse filter is capable of separating multiple input force signals even when the vibration signals contain reverberated information from the inputs in overlapping frequency ranges. The technique has been successfully applied to a flat plate system with two inputs and up to four vibration measurements. Guidelines are suggested for reducing the effects of measurement inaccuracies on the force predictions.

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On discrete band-limited signal extrapolation

Mathematical Analysis, Wavelets, and Signal Processing - Contemporary Mathematics ◽

10.1090/conm/190/02314 ◽

1995 ◽

pp. 323-337 ◽

Cited By ~ 18

Author(s):

Thomas Strohmer

Keyword(s):

Discrete Band ◽

Band Limited ◽

Signal Extrapolation

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Inverse Scattering Solutions by a Sinc Basis, Multiple Source, Moment Method -- Part II: Numerical Evaluations

Ultrasonic Imaging ◽

10.1177/016173468300500407 ◽

1983 ◽

Vol 5 (4) ◽

pp. 376-392 ◽

Cited By ~ 39

Author(s):

Michael L. Tracy ◽

Steven A. Johnson

Keyword(s):

Inverse Problem ◽

Inverse Scattering ◽

Scattering Problem ◽

Inverse Scattering Problem ◽

Incident Radiation ◽

Multiple Sources ◽

Reconstruction Quality ◽

Ill Posed ◽

Band Limited ◽

Pseudo Inverse

In part I, we presented a method for solving the inverse scattering problem using multiple sources and detectors. Allowance for multiple angles of incident radiation improves the ill-posed nature of the inverse problem by improving the quality and quantity of information gathered at detector points. This paper describes implementation and numerical evaluation of the method. An 11 by 11 image reconstructed from noisy scattered field data is shown to closely match the original scattering object, and the improvement possible by constraining the reconstruction to be spatially band limited is demonstrated. Furthermore, for a somewhat simpler “pseudo-inverse problem,” we give findings on the effects that detector radius, degree of overdetermination, noise, and object contrast have on reconstruction quality.

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