Abstract
In this work we present two sparse deconvolution methods for nondestructive testing. The first method is a special matching pursuit (MP) algorithm in order to deconvolve the mixed data (signal and noise), and thus to remove the unwanted noise. The second method is based on the approximate Prony method (APM). Both methods employ the sparsity assumption about the measured ultrasonic signal as prior knowledge. The MP algorithm is used to derive a sparse representation of the measured data by a deconvolution and subtraction scheme. An orthogonal variant of the algorithm (OMP) is presented as well. The APM technique also relies on the assumption that the desired signals are sparse linear combinations of (reflections of) the transmitted pulse. For blind deconvolution, where the transducer impulse response is unknown, we offer a general Gaussian echo model whose parameters can be iteratively adjusted to the real measurements. Several test results show that the methods work well even for high noise levels. Further, an outlook for possible applications of these deconvolution methods is given.
Highlights
Many ultrasonic testing applications are based on the estimation of the time of arrival (TOA), time of flight diffraction (TOFD) or the time difference of arrival (TDOA) of ultrasonic waves
Most deconvolution techniques have been constructed for a time-invariant linear convolution model of the form s(n) = x(n) ∗ f (n) + ν(n) with a time series x(n) containing the relevant information on reflectivity, the transducer impulse response represented by the system f (n), and a noise vector ν(n)
We have proposed two different deconvolution algorithms that both map an A-scan to a sparse vector that still contains the relevant information of the A-scan in an encoded form
Summary
Many ultrasonic testing applications are based on the estimation of the time of arrival (TOA), time of flight diffraction (TOFD) or the time difference of arrival (TDOA) of ultrasonic waves. In order to analyze the received signals, one can usually suppose that the diffracted and backscattered echo from an isolated defect is a time-shifted, frequencydissipated replica of the transmitted pulse with attenuated energy and inverted phase. In case of various flaw defects, the backscattered ultrasonic signal is a convolution of the modified pulse echo with the signal representing the reflection centers. We are faced with noisy measurements, where the noise is caused by reflections on microstructures of the tested material and electronic disturbances. Most deconvolution techniques have been constructed for a time-invariant linear convolution model of the form s(n) = x(n) ∗ f (n) + ν(n) with a (sparse) time series x(n) containing the relevant information on reflectivity, the transducer impulse response represented by the system f (n), and a noise vector ν(n). Blind deconvolution methods are of special interest, where one has
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