This paper deals with the time reversal approach along with signal classification using ϕ-divergences in biomedical applications for localization and statistical classification of ultrasonic nonlinearities. The time reversal (TR) approach in combination with nonlinear elastic wave spectroscopy (NEWS) is used to obtain the nonlinear signature of air bubbles with different sizes and ultrasound contrast agents in a liquid. An optimized chirp-coded signal in the range of 0.6–3 MHz is used as a compression coding. The signal classification is performed using the fuzzy classification method and the divergence decision tree algorithm using specific ϕ-divergence spectral measures extracted from the received ultrasonic response containing acoustic nonlinearities. The classification results prove that different types of nonlinearities extracted with classical “pulse inversion” based coding methods can be identified. Simultaneously, the different positions of scattered sources are distinguished by ϕ-divergence methods. The potential of time reversal nonlinear elastic wave spectroscopy methods for understanding of ultrasonic wave propagation in complex media is clearly exhibited.

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