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Signal denoising and ultrasonic flaw detection via overcomplete and sparse representations.

Sparse signal representations from overcomplete dictionaries are the most recent technique in the signal processing community. Applications of this technique extend into many fields. In this paper, this technique is utilized to cope with ultrasonic flaw detection and noise suppression problem. In particular, a noisy ultrasonic signal is decomposed into sparse representations using a sparse Bayesian learning algorithm and an overcomplete dictionary customized from a Gabor dictionary by incorporating some a priori information of the transducer used. Nonlinear postprocessing including thresholding and pruning is then applied to the decomposed coefficients to reduce the noise contribution and extract the flaw information. Because of the high compact essence of sparse representations, flaw echoes are packed into a few significant coefficients, and noise energy is likely scattered all over the dictionary atoms, generating insignificant coefficients. This property greatly increases the efficiency of the pruning and thresholding operations and is extremely useful for detecting flaw echoes embedded in background noise. The performance of the proposed approach is verified experimentally and compared with the wavelet transform signal processor. Experimental results to detect ultrasonic flaw echoes contaminated by white Gaussian additive noise or correlated noise are presented in the paper.