Novel Impact Echo Imaging Technique Using Multiresolution
in Temporal and Spatial Domains
Amjed S. Al-Fahoum and Ali M. Reza
Department of Electrical Engineering and Computer Science
University of Wisconsin-Milwaukee
P. O. Box 784, Milwaukee WI 53201-0784
Abstract Echo imaging techniques have been shown to be effective in both demonstrating the reflectivity patterns and detecting different kind of flaws in many engineering fields. Further modifications in such approaches depend solely on the variability of the medium under investigation, the temporal resolution of the source waves and the spatial resolution of the source-receiver array. Impact echo imaging aimed at high resolution gains using conventional processing techniques (deconvolution and migration) suffers from inherent problems such as noise degradation, nonstationarity of the mediums, incompleteness of the data set, and exactness of the modeling parameters. In this work, we intuitively propose a new imaging approach that employs the apriori knowledge of the medium to predict a robust modeling structure of the medium. This model will then be used in an optimum way to minimize the squared error between the observed data and the exact medium. To guarantee a solution for this ill posed inverse problem, the exact medium is constrained to satisfy the predicted model and the normal equations resulted from this minimization process are weighted by a positive definite function to maintain stability and prevent divergence. To achieve high temporal resolution, we utilize from the ability of wavelet transform in decomposing the data into non-overlapping spectral bands and performing both time varying spectral prewhitening and adaptive deconvolution to suppress the source signature. For high spatial resolution, we will perform the constrained estimation approach in each sub-domain to minimize the computational effort. To evaluate the performance of the proposed approach, we will conduct a comparative study that manifests the achievements and the limitations of this approach over the conventional echo imaging techniques. To demonstrate the effectiveness of our approach in handling near field and far field problems, we apply this technique to detect various flaws in post-tensioned concrete bridge structures.
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