Contrast Improvement in Sub- and Ultraharmonic Ultrasound Contrast Imaging by Combining Several Hammerstein Models

Abstract

Sub- and ultraharmonic (SUH) ultrasound contrast imaging is an alternative modality to the second harmonic imaging, since, in specific conditions it could produce high quality echographic images. This modality enables the contrast enhancement of echographic images by using SUH present in the contrast agent response but absent from the nonperfused tissue. For a better access to the components generated by the ultrasound contrast agents, nonlinear techniques based on Hammerstein model are preferred. As the major limitation of Hammerstein model is its capacity of modeling harmonic components only, in this work we propose two methods allowing to model SUH. These new methods use several Hammerstein models to identify contrast agent signals having SUH components and to separate these components from harmonic components. The application of the proposed methods for modeling simulated contrast agent signals shows their efficiency in modeling these signals and in separating SUH components. The achieved gain with respect to the standard Hammerstein model was 26.8 dB and 22.8 dB for the two proposed methods, respectively.

Complexity reduction of ultrasound sub-ultra-harmonic modeling by an input modified volterra approach

“…Experiments are carried out by using the same experimental used in [17]. The excitation signal is transmitted to a 10 MHz PZT single element.…”

“…The main drawback of MISO Volterra methods is the large number of kernels to be evaluated, which leads to a high computational cost. However, other proposed solutions are based on the use of Hammerstein model [17], [18]; they allow the extraction of sub and ultra-harmonic components. Unfortunately, it is only possible by restraining the assumptions on the model.…”

Evaluation of estimated hammerstein models via normalized projection misalignment of linear and nonlinear subsystems

“…Now forming the NOE quotient according to (3), and immediately substituting filter-and function-norm ratios, (10) and (13), we arrive at the desired relationship between the Hammerstein normalized output-error and our projection-misalignment quantities,…”

“…The parametric Hammerstein model, as a special case of the Volterra series [7], exhibits linearity in all coefficients too. Applications are found in audio and acoustic signal processing [10,11], sound and vibration [12], medical ultrasound [13], biological [14,15] or chemical modeling [16], to name just a few.…”

Harmonic magnification by time reversal based on a Hammerstein decomposition

“…To understand it, one way consists in modelling the ultrasound system by simple parallel subsystems. Such model as a Hammerstein system is sufficient to describe the nonlinear behaviour [10], [11]. Thus the system usually can be decomposed by parallel subsystems where the nonlineary is separated of the linearity.…”