Ultrasonic Imaging in Highly Attenuating Materials With Hadamard Codes and the Decomposition of the Time Reversal Operator

In this paper, defects in a high density polyethylene pipe are imaged with the total focusing method. The viscoelastic attenuation of this material greatly reduces the signal level and leads to a poor signal-to-noise ratio (SNR) due to electronic noise. To improve the image quality, the decomposition of the time reversal operator method is combined with the spatial Hadamard coded transmissions before calculating images in the time domain. Because the Hadamard coding is not compatible with conventional imaging systems, this paper proposes two modified coding methods based on sparse Hadamard matrices with +1/0 coefficients. The SNRs expected with the different spatial codes are demonstrated, and then validated on both simulated and experimental data. Experiments are performed with a transducer array in contact with the base material of a polyethylene pipe. In order to improve the noise filtering procedure, the singular values associated with electronic noise are expressed on the basis of the random matrix theory. This model of noise singular values allows a better identification of the defect response in noisy experimental data. Finally, the imaging method is evaluated in a more industrial inspection configuration, where an immersion array probe is used to image defects in a butt fusion weld with a complex geometry.