## 1 Introduction  
Ultrasound imaging is an essential clinical tool for screening tissue structures. The intensity of an ultrasound grayscale image (B-mode) is determined based on the amplitude of the backscattered signals resulting from the interactions between acoustic scatterers and the incident wave. When the degree of an acoustic impedance mismatch is increased, the signal amplitude and the corresponding B-scan brightness increase accordingly. In clinical settings, B-scan brightness is generally used to describe the echogenicities of the scatterers in a tissue for diagnosis. Although several functional imaging techniques are available in current ultrasound systems, the conventional B-scan is still widely adopted as a convenient screening tool for describing echogenicity in clinical evaluation [1; 2; 3; 4; 5], because diseases typically accompany changes in acoustic properties of scatterers in tissues (e.g., liver steatosis or muscle fibrosis) [3; 4; 5]. In addition to the effects of an acoustic impedance mismatch, the brightness of B-scans depends on system factors such as system gain, time gain compensation (TGC), log compression, and signal/image processing; among these, system gain is a dominant factor for determining the amplitudes of received signals and the corresponding image brightness. The most frequent problem in clinical settings entails different users using different gains for screening, thus resulting in varied explanations for the echogenicity of examined tissues. In some conditions, the above problem may be overcome by normalizing the intensity with the background image data (e.g., liver-to-kidney intensity ratio for fatty liver assessment). However, for different types of tissues, it is not necessary to have appropriate background information that can be used for normalization. This might explain why researchers cannot reach a definitive diagnosis when using B-scans alone. Thus, establishing an objective index or a measurement protocol that is independent of the system gain is essential when describing tissue echogenicity by using B-scans in routine clinical examinations. However, no relevant studies have explored this concern. This paper addresses the following fundamental question: Can the image intensity measure be independent of the system gain? Understanding the ultrasound backscattered signal model may be an effective foundation for answering the posed question. Previous studies have described that under ideal conditions, ultrasound backscattered signals \(s(t)\) can be modeled as a result of the convolution of the incident wave with the tissue function [6; 7; 8],  
\[s(t)=h(t)\otimes z(t) \tag{1}\]  
where \(h(t)\) represents the transfer function of the transducer (i.e., the incident wave), and \(z(t)\) denotes the spatial distribution function of the scatterers. After amplification by using an ultrasound system, the following equation is obtained:  
\[s(t)=G\times[h(t)\otimes z(t)] \tag{2}\]  
where \(G\) denotes the system gain. Apparently, a gain effect was intrinsic to the signals output from a system and therefore unavoidable. We assume that signal processing based on self-decomposition and normalization may provide an effective solution to eliminating the gain effect from the ultrasound echo measurements. The reason is explained as follows. Signal self-decomposition produces several sub-signals with the same gain effect, and these sub-signals can be used for normalization to eliminate the gain effect. In the meantime, the signal normalization results must contain physical meanings associated with \(h(t)\) and \(z(t)\) to enable describing the tissue echogenicity. Therefore, selecting an appropriate decomposition method for signal normalization may be critical to satisfy these requirements. Recently, the Hilbert-Huang Transform (HHT) has become a highly attractive time-frequency analysis method for nonlinear and non-stationary data [9; 10; 11; 12]. In the HHT, an empirical mode decomposition (EMD) was developed for meaningfully determining the instantaneous frequency of a signal.