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.

Figure 1

Block diagram of second harmonic imaging.

Figure 2

Block diagram of subultraharmonic imaging.

Figure 3

Block diagram of Hammerstein model.

Figure 4

Block diagram of method  1, modeling by input frequency downshifting.

Figure 5

Block diagram of method  2: modeling by output frequency shifting.

Figure 6

(a) Comparison between the signal backscattered by the contrast agent y(n) (in black) and its estimation $\widehat{y}(n)$ (in green): the signal modeled with (top) the standard Hammerstein model, (middle) method  1, and (bottom) method  2. (b) Spectra of different signals presented in (a). Here SNR = ∞ dB.

Figure 7

(a) Comparison between the backscattered difference signal between the backscattered signal by the contrast agent (black) and the SUH signal (green) modeled with (top) method  1 and (bottom) method  2. (b) Spectra of different signals presented in (a). Here SNR = ∞ dB.

Figure 8

Variation of RMSE in dB between the backscattered signal by the contrast agent and that modeled with (blue) the standard Hammerstein model, (black) method  1, and (green) method  2 as a function of the memory of Hammerstein model in presence of output noise: SNR = ∞ dB, SNR = 20 dB, SNR = 15 dB, and SNR = 10 dB.