## 3 Materials and Methods
### Experiments on Lipid Phantoms  
Experiments on phantoms with different behaviors of echogenicity were performed. The phantom was prepared by boiling the agar-water mixture (dissolving 1.5 g of agar powder in 200 mL of water) and cooling it to form a solid gel. The graphite powder with <20-\(\upmu\)m particles (Model 282863, Sigma-Aldrich, St. Louis, MO, USA) was added to the phantom to simulate the scatterers in tissue. The number density of the scatterers in the phantom was 128 scatterers/mm\({}^{3}\), which was adequately large to produce a fully developed speckle pattern in a B-mode image. To further produce different image intensities of the B-scan, various proportions of soybean-oil lipid emulsion (Intrafat, Nihon Pharmaceutical Industry, Osaka, Japan) were added to the phantoms to produce varying degrees of attenuation, as presented in Figure 1a,b. The lipid concentrations ranged from 0% to 30%, corresponding to the range of attenuation coefficient from 0.684 to 1.108 dB/cm\(\cdot\)MHz (the attenuation coefficient of each phantom was calculated using the standard substitution method). A previous study reported that when the lipid concentrations are increased, the brightness of the B-scan decreases accordingly [15]. In total, six independent phantoms were prepared for each lipid concentration (\(n=36\)). A commercial ultrasound scanner (Model 3000, Terason, Burlington, MA, USA) was used to scan the phantoms. The applied probe was a wideband linear array with a central frequency of 7 MHz and 128 elements (Model 10L5, Terason). An agar phantom with the same graphite powder concentrations was prepared to calibrate the gain setting in the imaging system. A cyst was created as an anechoic region in the center of the phantom, and the image intensities, calculated using the square of the envelope amplitude, corresponding to the cyst and the phantom background were used to estimate the SNRs, as shown in Figure 1c. The calibration results obtained from six independent measurements are shown in Figure 1d. When the digital gain index in the system was adjusted from 1 to 6, the SNRs produced ranged from 12 to 33 dB, which was used as the range of gain applied to the phantom scanning. Each lipid phantom was immersed in a water tank and scanned using the ultrasound system with different system gains that ranged from 12 to 33 dB. The image raw beamformed radiofrequency (RF) data were acquired from the phantom at a 30-MHz sampling rate. In total, the image comprised 128 scan lines of the backscattered echoes, corresponding to a size of 3 \(\times\) 3.5 cm (depth \(\times\) width). The image scan lines were demodulated using the absolute value of the Hilbert transform to obtain the envelope image, which was then normalized and compressed using logarithmic calculations to obtain the B-mode image at a dynamic range of 40 dB (i.e., the pixel values range between 0 and 40 dB). Concurrently, the raw RF image data were decomposed into the IMFs by using a two-dimensional (2D) EMD, which was developed by [PERSON] et al. [16] for image EMD processing. After applying 2D EMD on the RF signals, each IMF signal was demodulated and log-compressed to display the IMF-based B-mode images (i.e., \(C_{1}\), \(C_{2}\), \(\ldots\), \(C_{i}\) images).