Compressive sensing with warped frequency models in lamb waves damage detection procedures

Compressive Sensing (CS) has emerged as a potentially viable technique for the efficient acquisition of high-resolution signals that have a sparse representation in a fixed basis. In this work, we have developed a general approach for low rate sampling and efficient CS impulse response recovery algorithms that exploits convolution signal models of dispersive ultrasonic guided waves with a sparse representation in the frequency warped basis. We apply our framework to both to lower the sampling frequency and to enhance defect localization performances of Lamb wave inspection systems. The reconstruction algorithm is based on both the iterative support estimation and alternating minimization algorithm to further improve localization accuracy, separating the contribution of the exciting wave. As a result, an automatic detection procedure to locate defect-induced reflections was demonstrated and successfully tested on experimental Lamb waves propagating in an aluminum plate.