Compressive sensing for direct time of flight estimation in ultrasound-based NDT

This paper presents an approach for estimation of ultrasonic time-of-flight (TOF) within a Non Destructive Testing (NDT) and Structural Health Monitoring (SHM) context. The presented method leverages recent advances in the field of Compressive Sensing (CS), which makes use of sparsity in a transform domain of a signal in order to reduce the number of samples required to store it. CS achieves this through a two key ideas: random matrix projections, and l1-penalised linear regression. In this case, sparsity arises from the observation that in a pulse-echo ultrasound test, the number of echoes is relatively small compared to the number of measurement points in a waveform. This sparsity is evident in the autocorrelation of ultrasound waveforms. A method is suggested in this paper for building suitable basis functions, based on Hankel matrices, which transform a signal into its autocorrelation domain. It is shown how this can be combined with standard CS techniques in order to achieve a very low error in TOF estimates with up to one-tenth of the original ultrasound samples.