## 1 Introduction  
Hepatic steatosis, a condition where excess fat accumulate within the hepatocytes, is a key manifestation of non-alcoholic fatty liver disease (NAFLD). With the growing epidemic of obesity, the incidence of NAFLD has significantly increased in the past decades, with a prevalence reported to be 6-35% (median 20%) worldwide [1]. NAFLD may progress to non-alcoholic steatohepatitis (NASH), causing chronic inflammation of the liver parenchyma, which may develop into a fibrosis, a cirrhosis, or a liver cancer. Therefore, early detection of hepatic steatosis is of critical importance.  
Currently, liver biopsy is the clinical golden standard for hepatic steatosis assessment. However, liver biopsy is invasive and associated with sampling errors. Medical imaging has become a noninvasive alternative to liver biopsy; the modalities include computed tomography (CT), magnetic resonance (MR) spectroscopy, MR imaging, and ultrasound imaging [2]. MR spectroscopy-derived proton-density fat fraction (PDFF) is currently accepted as the noninvasive reference standard for hepatic steatosis quantification [2,3]. However, MR and CT are expensive with limited availability, and CT involves the use of radiation. Compared to CT and MR, ultrasound imaging has advantages of low cost, wide availability, and real-time capability [4, 5, 6]. Ultrasound has been recommended as a first-line diagnostic test for the management of NAFLD [7].  
Ultrasound imaging involves a transducer transmitting ultrasound waves into a tissue being interrogated. The incident waves interact with the tissue and the transducer receives backscattered signals (Figure 1). B-mode (Brightness-mode) ultrasound imaging, which is based on the amplitude of the envelope of beamformed radiofrequency (RF) signals, is frequently used in clinical routine for the assessment of hepatic steatosis. Additionally, B-mode ultrasound image processing techniques, including deep learning [8,9], have been investigated for characterizing hepatic steatosis. However, B-mode ultrasound is qualitative and can be affected by factors including image post-processing parameters. Quantitative ultrasound (QUS) [10] aims to extract quantified acoustic parameters from the ultrasound backscattered signals for ultrasound tissue characterization. QUS has been explored for evaluating hepatic steatosis, including speed of sound [11,12], ultrasound attenuation [13,14], backscatter coefficient [14], and shear-wave dispersion [15].  
Acoustically, a liver tissue can be thought of as a collection of ultrasound scatterers [16]. The ultrasound backscattered signals are a spatial summation of the scattered waves contributed by each scatterer. QUS envelope statistics [17] extracts statistical information from the envelope of backscattered RF signals and is related to liver tissue microstructures. Envelope statistics techniques, both statistical model-based [18, 19, 20] and non-model-based [21, 22], have shown potential for hepatic steatosis characterization. However, a state-of-the-art review of hepatic steatosis assessment using envelope statistics techniques is still lacking.  
In this paper, envelope statistics-based QUS parametric imaging techniques for characterizing hepatic steatosis are reviewed and discussed. Future developments are also suggested. The remainder of this paper is arranged as follows. In Section 2, the algorithmic steps for ultrasound envelope statistics parametric imaging will be introduced. Then, statistical model-based and non-model-based ultrasound envelope statistics parametric imaging techniques for hepatic steatosis assessment will be  
Figure 1: Ultrasound scattering and brightness mode (B-mode) image formation.  
reviewed in Sections 3 and 4. A discussion on state-of-the-art techniques and future developments will be made in Section 5.