Sparse Deconvolution Methods for Ultrasonic NDT

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. Fur

An adaptive sparse deconvolution method for distinguishing the overlapping echoes of ultrasonic guided waves for pipeline crack inspection

“…In [12], sparse deconvolution techniques based on l 1 and l 0 regularizations were employed to solve the resolution enhancement problem of the acoustic signal. Both the MP and the approximate Prony sparse deconvolution methods are presented in [13], and the test results indicate that the methods perform well, even for high noise levels. Other sparse deconvolution methods have also been developed to obtain a sparse solution.…”

Improved Denoising Method for Ultrasonic Echo with Mother Wavelet Optimization and Best-Basis Selection

“…In that paper, an ideal band-pass filter was implemented over common wavelet thresholding process. In [35], the authors presented two sparse deconvolution methods for NDT testing. The first method called "MP" is a special matching pursuit algorithm for deconvolving the noisy data.…”

Approximation performance of model functions for blind deconvolution of ultrasonic reflections

“…Estimation of the aforementioned parameters for the single echo does not present significant problem, but when several reflectors are present along the wave path the reflections pile up obscuring the reliable estimation of the echoes parameters [5]. If probing signal is of indefinite bandwidth such problem does not exist, but bandwidth is always limited in practice [6,7]. Furthermore, limited bandwidth is usually desirable, because signal acquisition system requirements can be relaxed [8], attenuation of ultrasound at high frequencies produces structural noise and signal degradation [9].…”

“…Iterative deconvolution techniques allow for efficient signal decomposition either processing one reflection at a time or several reflections simultaneously [6,10,12,15]. Yet, production of the reference signal constitutes a major problem in all deconvolution methods [5,6,16,17]. Signal spectral content is altered along the propagation path or at reflection interface [4].…”

“…Together with noise present, this significantly degrades the results of deconvolution. Blind deconvolution [17,18] is offering a production of reference signal using some simple mathematical model function, Gabor (harmonic oscillation with Gaussian envelope) being the most frequently used [6,19]. Result of such deconvolution significantly improves the SNR, adapts the signal spectral content changes and significantly reduces the required amount of computer memory needed to store or transmit the acquired data [20] by compressive sensing.…”