An approach to robust deconvolution of ultrasonic pulse-echo signals

The received signal in ultrasonic pulse-echo data in NDT can be modeled as a convolution between the transducer's impulse response and the reflection sequence that is the impulse characteristic of the inspected object. The deconvolution problem is typically formulated as estimation of the reflection sequence. The estimation task is often solved using linear minimum mean square error (MMSE) estimators that require accurate measurements of the transducer's impulse response. Measurement errors caused by non-ideal transducer measurement setup may degrade accuracy of the reflection sequence estimates. This paper describes a way of designing linear MMSE estimators with improved robustness against transducer impulse response measurement errors. The presented approach is based on the assumption that the impulse response can be determined with an error within a so-called uncertainty set, defined based on a physical model of the impulse response measurement, prior knowledge about the inaccuracies usually present in the measurement setup, and the available knowledge about the transducer. Robust linear MMSE estimators for the reflection sequence are proposed that minimize the mean squared error averaged over the uncertainty set. The robustness of the estimator is verified experimentally.