Wavelets and Their Application to Digital Signal Processing in Ultrasonic NDE

As the use of digital based ultrasonic testing systems becomes more prevalent, there will be an increased emphasis on the development of digital signal processing techniques. In the past, various Fourier based digital signal processing approaches have been formulated and applied in the ultrasonic nondestructive evaluation (NDE) research community. In many cases, the inherent inability of Fourier methods to handle non-stationary signals has been exposed as the Fourier methods are applied to non-stationary ultrasonic signals. Our intent is to investigate the application of wavelet based signals processing techniques to a variety of problems in ultrasonic NDE. Wavelet methods have a number of potential advantage over Fourier methods including the inherent ability of wavelets to deal with non-stationary signals.

[1]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[2]  J. Goodman.  Introduction to Fourier optics , 1969 .

[3]  Ill-Posedness, Regularization and Number of Degrees of Freedom , 1981 .

[4]  Leonard J. Y. Schulman,et al.  Communication in the presence of noise , 1992 .

[5]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Michael Frazier,et al.  A new transform for time-frequency analysis , 1992, IEEE Trans. Signal Process..

[7]  Ph. Tchamitchian,et al.  Wavelets: Time-Frequency Methods and Phase Space , 1992 .

[8]  Brian DeFacio,et al.  Wavelet version of Fourier optics , 1990, Optics & Photonics.

[9]  Arthur F. Gmitro,et al.  Digital Image Synthesis and Inverse Optics , 1990 .

[10]  Steven P. Neal,et al.  A prior knowledge based optimal Wiener filtering approach to ultrasonic scattering amplitude estimation , 1989 .

[11]  R. Landauer.  Information is physical , 1991 .

[12]  J. Morlet,et al.  Wave propagation and sampling theory—Part II: Sampling theory and complex waves , 1982 .

[13]  M. Wickerhauser.  Acoustic signal compression with wavelet packets , 1993 .

[14]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[15]  The role of filters and the singular-value decomposition for the inverse Born approximation , 1986 .

[16]  B. Jawerth,et al.  A discrete transform and decompositions of distribution spaces , 1990 .

[17]  Richard H. Sherman,et al.  Chaotic communications in the presence of noise , 1993, Optics & Photonics.

[18]  J. Morlet,et al.  Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media , 1982 .

[19]  Dennis Gabor,et al.  Theory of communication , 1946 .