AN APPLICATION OF WAVELET SIGNAL PROCESSING TO ULTRASONIC NONDESTRUCTIVE EV ALUA TION Alan Van Nevel and Brian DeFacio Department of Physics and Astronomy University of Missouri-Columbia Columbia, MO 65211 Steven P. Neal Department of Mechanical and Aerospace Engineering University of Missouri-Columbia Columbia, MO 65211 INTRODUCTION In this paper we present a flaw signature estimation approach which utilizes the Wiener filter [1-5] along with a wavelet based procedure [6-15] to achieve both deconvolution and reduction of acoustic noise. In related ealier work by Patterson et al. [6], the wavelet transform was applied to certain components of the Wiener filter, and coefficient chopping was used to reduce acoustic noise. In the approach that we present here, the wavelet transform is applied individually to the real part and to the imaginary part of the scattering amplitude estimate determined by application of a sub-optimal form of the Wiener filter. This wavelet transform takes the real and imaginary parts, respectively, from the typical Fourier frequency domain to a wavelet phase space. In this new space, the acoustic noise shows significant separation from the flaw signature making selective pruning of wavelet coefficients an effective means of reducing the acoustic noise. The final estimates of the real and imaginary parts of the scattering amplitude are determing via an inverse wavelet transform. The remainder of the paper begins with a section on wavelets that is intended to provide a brief review for the reader already familiar with wavelets and to provide a list of references for those who would like to learn more about wavelets. The model for a noise- corrupted flaw signal is then presented along with a review of Wiener filter based deconvolution. The wavelet signal processing approach is then described. Various wavelet families and coefficient pruning schemes are summarized via tables of Ll error norms along with graphical presentation of scattering amplitude estimates. The paper closes with a discussion of results. WAVELETS In the past ten years, a new family of functions, known as wavelets, has been created [10,11,13]. Wavelets are bases (linearly independent sets of generators) or frames (bases plus some repeated elements) for infinite dimensional function spaces of finite energy, causal signals. In this work, our attention will be restricted to orthonormal bases. Review a[Progress in Quantitative Nondestructive Evaluation, Vol, 15 Edited by 0,0, Thompson and D,E, Chimenti, Plenum Press, New York, 1996 733