The program include an example in the file "test.m". The modelisation is then realized from the Hammerstein structure.
IEEE Wireless Communications Letters (2022)
Badarneh Osamah
By Ménigot Sébastien, Kanbar Emma, Bouakaz Ayache, and Girault Jean-Marc
Working Paper (2016)
Nowadays, ultrasound imaging contrast has enhanced the contrast thanks the nonlinear behavior of microbubbles. Unfortunately, this contrast improvement is comprised by the nonlinear acoustic propagation in tissue. However, microbubbles can also oscillate with a f0/2-subharmonic frequency. Therefore, as there is no subharmonic in the tissue backscattering, the subharmonic imaging could increase the contrast highly. However, the subharmonic extraction can be more or less empirical by using standard filters. The aim of this study is thus to propose an optimal extraction of subharmonics. Hammerstein model showed a high efficiency in modelling nonlinear systems. However, it is unable to model subharmonics. We propose two solutions by changing the input or the output of the Hammerstein model. Experiments are carried out by transmitting ultrasound wave at 10 MHz to a water-diluted solution of Sonovue. The nonlinear microbubble responses were measured by a 5 MHz transducer. Results showed that the error between the experimental signal and the modeling signal was less than -18 dB. Moreover, the bias was always less than -15 dB. Finally, the signal-to-noise ratio could be increase by 4 dB in comparison with a standard filtering. Thanks to the modified Hammerstein model, it was possible to set the extraction optimally adjusted to the subharmonic components. No manual analysis of the signals was required.
Ménigot S., Kanbar E., Bouakaz A., and Girault J. (2016) SNR Improvement by Subharmonic Extraction with Hammerstein Models for Microbubble Signals . Working Paper.