Overlapping of reflected ultrasonic echoes is a universal physical phenomenon, when the measured thickness is less than a limit threshold (e.g. 1mm for metallic materials using conventional processing methods). Generally, two typical signal states may be generated in this situation: highly overlapping and distorted overlapping. If the overlapping echoes cannot not be separated precisely, significant measurement errors will inevitably occur. In this research, an improved matching pursuit method for overlapping echo separation has been developed. To approximate the overlapping echoes, a dictionary composed of atoms with truncated Nakagami functions is constructed to replace the commonly used model, which considers scattering conditions. Furthermore, an atomic selection principle combining preselection of the remainder L2 norm and minimum L1 norm of the residual signal is presented. To reduce the correlation of the residual error in iterations and ensure the correct separation of echoes in order, the ultrasonic signal is truncated for matching based on short-time Fourier transform (STFT) analysis. Compared with some competing methods, the proposed method shows superiority in handling highly overlapping echoes and distorted echoes in both simulation and experiments of ultrasonic thickness measurement.
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