Echo parameter estimation for ultrasonic NDE applications via a two-step compressed sensing

The recently developed compressed sensing (CS) framework has been applied to various data intensive imaging applications. It provides significant reductions in sampling rate with minimal loss in image quality. In this investigation, a CS-based sampling scheme is introduced for ultrasonic nondestructive evaluation (NDE) signals. The feasibility of parameter estimation based on the new sampling method is explored. Especially, a two-step compressed sensing with Gaussian chirplet model is proposed for data acquisition and echo parameter estimation. The CS framework is utilized to estimate the time-of-arrivals (TOAs) of chirplets. With the estimated TOAs, another iteration of data acquisition is performed to acquire the echo amplitude accurately. It has been shown that the two-step CS can estimate the TOAs of ultrasonic echoes with high accuracy in the presence of noise with SNR as low as -5 dB. Furthermore, the estimation is robust to inaccurate knowledge of the transducer bandwidth.