Sub and ultra harmonic extraction using several Hammerstein models

Ultrasound contrast imaging has been introduced in order to increase the contrast of echographic images by injecting microbubbles in the vascular system. They are gas filled microbubbles with nonlinear behavior. One of the most used modality of ultrasound contrast imaging is the second harmonic imaging. This imaging technique, based on the reception of the second harmonic, is devoted to image only the nonlinearity of the microbubble. However, in such ultrasound images the contrast is limited by the nonlinear components of non-perfused tissue. Sub and ultra harmonic imaging appeared to be an interesting alternative to overcome this limitation since, unlike tissue, microbubbles generate sub and ultra harmonics. In order to extract optimally these sub and ultra harmonic components, we proposed a new model based on several Hammerstein models able to model and extract sub and ultra harmonics. Results showed i) that microbubble signal is accurately represented both in time and frequency domains and ii) that sub- and ultra-harmonics were well extracted and separated from harmonic component. Note that the gain achieved by comparing the filtering signals with our method and the standard Hammerstein was 4.6 dB.