## 4 Results  
Figure 4 shows the backscattered signals \(s(t)\) with different gain factors obtained from simulations and the corresponding IMFs after applying EMD of \(s(t)\). In practice, the ratios of amplitude between different IMFs may depend on the degree of noise interference on the signal. However, while using the raw backscattered signals without any postprocessing for EMD, the primary components of the original signals were assigned to the first and second IMFs. The quantitative analysis of the signals showed that the \(C_{1}\) and \(C_{2}\) account for up to 90% of the amplitude of the backscattered signals, as shown in Figure 5. This finding agreed well with the previous study [14], supporting the selection of \(C_{1}\) and \(C_{2}\) for the definition of the IER. Moreover, the results in Figure 4 further showed that the summation of each IMF multiplied by the gain factor equals the signal multiplied using the same gain, demonstrating the reasonability of Equations (12) and (13). Figure 6a-f present the B-mode images and the corresponding \(C_{1}\), \(C_{2}\), \(C_{3}\), and \(C_{4}\) images of the phantoms with varied lipid concentrations ranging from 0% to 30%. The speckle patterns in the B-mode images of different phantoms were similar because the number density of the scatterers in each phantom was set the same.For each lipid concentration, the speckle pattern of the \(C_{1}\) image was similar to that of the B-mode image. Notably, the EMD decomposed image data to produce the IMFs from high- to low-frequency components. The first IMF was the data with the highest-frequency components compared with the other IMFs; therefore, the signal waveforms in the \(C_{1}\) image were similar to those of the original backscattered RF echoes but more symmetrical in the upper and lower envelopes [14; 17]. This also explains why the other IMF-based images (\(C_{2}\), \(C_{3}\) and \(C_{4}\) images in Figure 6) exhibited poorer spatial resolutions compared with the \(C_{1}\) image. Figure 4: The backscattered signals \(s(t)\) with different gain factors obtained from simulations and the corresponding IMFs after applying EMD of \(s(t)\). The summation of each IMF multiplied by the gain factor equals the signal multiplied using the same gain factor. Figure 5: The percentage of amplitude of each IMF compared with that of the original backscattered signal (obtained from ten independent simulations). The first and second IMFs account for up to 90% of the amplitude of the backscattered signals. Figure 6: B-mode and C\({}_{1}\)–C\({}_{4}\) images of the phantoms with lipid concentrations ranging from 0% to 30%. (**a**) 0%, (**b**) 5%, (**c**) 10%, (**d**) 15%, (**e**) 20% and (**f**) 30%. B-mode and IMF-based images are constructed using the log-compressed envelopes of the RF and IMF data obtained from the EMD. ROI: region of interest. The \(C_{1}\) image intensities were observed as a function of the lipid concentrations obtained using gains ranging from 12 to 33 dB (Figure 7a). At 33-dB gain, the \(C_{1}\) intensity decreased from 185.89 \(\pm\) 19.74 to 61.91 \(\pm\) 3.09 when the lipid concentrations were increased. Because of the extreme resemblance between the \(C_{1}\) and the RF signals, the \(C_{1}\) image intensity could be considered as that measured using the RF data. When the gain decreased to 12 dB, the \(C_{1}\) intensity decreased from 76.31 \(\pm\) 7.72 to 26.46 \(\pm\) 1.12 in the same range of lipid concentrations. As shown in Figure 7b, when the system gain decreased to 12 dB, the average error for the various lipid concentrations was larger than 50%. Note that the \(C_{1}\) image findings were also observed in the \(C_{2}\) image, as shown in Figure 7c,d. The \(C_{2}\) intensities measured using 33 and 12 dB decreased from 27.92 \(\pm\) 2.59 to 15.58 \(\pm\) 0.56 and from 12.26 \(\pm\) 0.94 to 7.78 \(\pm\) 0.27, respectively; the measurement error at 12 dB was also \(>\)50%. These results demonstrated that the intensity measurement was significantly affected by the gain effect.