Sparse deconvolution method for improving the time-resolution of ultrasonic NDE signals

The estimation of the time-of-arrival (TOA) and/or time-of-flight (TOF) of the ultrasonic echoes is essential in ultrasonic non-destructive evaluation. In this paper, a sparse deconvolution method is proposed for deconvolving ultrasonic signals. To obtain the transducer pulse-echo wavelet, matching pursuit (MP) method has been used to analyze noisy ultrasonic pulse-echo wavelet and decompose the noisy pulse-echo wavelet into unit-norm vectors, then, the approximation pulse-echo wavelet obtained by the reconstruction result with several large coefficient decomposed unit-norm vectors. A weighting matrix is the central to the efficiency of the sparse deconvolution method. It increases the sparsity of the deconvolution result and decreases the influence of the added noise. The deconvolution gives high-resolution ultrasonic reflectivity function. We can obtain the accurate TOA or TOF from the ultrasonic reflectivity function. Results using real ultrasonic data show the sparse deconvolution method yields good estimates of the spikes associated with the reverberation echoes and the thickness of a steel sample can be calculated by the ultrasonic reflectivity function with a reasonable accuracy.