Our overall objective is to improve the spatial resolution of ultrasonic images used for quantitative non-destructive evaluation of materials. These images contain distortion due to the band-pass frequency responses of the associated transducers and propagation paths. Our specific objective is to estimate the impulse responses of flaws and interfaces in material samples. Thus, we are attacking the restoration problem, which is, in general, ill-posed and difficult to solve in practice. We have applied several techniques for regularizing the problem, including both time- and frequency-domain methods, and some constrained optimization algorithms. Our new results demonstrate that regularization techniques can allow successful, practical solutions to this ill-posed problem. Our work concentrates mainly upon the problem in which the impulse response is expected to be impulsive (consisting of a weighted sum of delayed impulses). Our results show that some problems of practical interest are tractable by using a two-step procedure involving first system identification and then spectrum extrapolation to obtain sharper spatial impulses. The paper presents the results of experiments using actual laboratory signals, in which we demonstrate improved spatial resolution for impulsive signals, allowing more meaningful interpretation of ultrasonic A- and B-scans.
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