Semi-sparse deconvolution robust to uncertainties in the impulse responses

The received signal in ultrasonic pulse-echo inspection can be modeled as a convolution between an impulse response, or prototype, and the reflection sequence that is the impulse characteristic of the inspected object. Deconvolution aims at approximately inverting this process to improve the time resolution so that the overlap between echoes from closely spaced reflectors becomes small. For the relatively high contrast reflection sequences often found in non-destructive testing applications, semi-sparse deconvolution algorithms will typically yield better results than the classical Wiener filter solution. However, this requires a prototype that is a good representative for all echo responses found in the signals. Since, in practice, the prototype is often chosen by the operator directly from the inspection data, the prototype may incidentally be a bad representative for modeling the echoes for the remaining part of the object. Because of the sensitivity to deviations in the prototype this can yield deconvolution results with poor reproducibility. This paper presents a new semi-sparse deconvolution algorithm that is robust to deviations in the prototype. The new robust algorithm is based on a modification of an earlier presented non-robust semi-sparse algorithm. The robustness is obtained by including a stochastic model of the variations in the prototypes to the signal model when deriving the algorithm. Experiments performed using simulated data verify that the robust algorithm is less sensitive to deviations in the prototypes compared to the non-robust version of the algorithm and show that the proposed algorithm yields better estimates than its non-robust version and the Wiener filter in scenarios for which the algorithm was derived. Results using real ultrasonic data further show that the algorithm can be useful in practical scenarios where similar deconvolution results are required from slightly different echoes.