Effects of Estimators on Ultrasound Nakagami Imaging in Visualizing the Change in the Backscattered Statistics from a Rayleigh Distribution to a Pre-Rayleigh Distribution

Abstract

Ultrasound Nakagami imaging has recently attracted interest as an imaging technique for analyzing envelope statistics. Because the presence of structures has a strong effect on estimation of the Nakagami parameter, previous studies have indicated that Nakagami imaging should be used specifically for characterization of soft tissues with fewer structures, such as liver tissues. Typically, changes in the properties of the liver parenchyma cause the backscattered statistics to transform from a Rayleigh distribution to a pre-Rayleigh distribution, and this transformation can be visualized using a Nakagami imaging technique. However, different estimators result in different estimated values; thus, the performance of a Nakagami image may depend on the type of estimator used. This study explored the effects of various estimators on ultrasound Nakagami imaging to describe the backscattered statistics as they change from a Rayleigh distribution to a pre-Rayleigh distribution. Simulations and clinical measurements involving patients with liver fibrosis (n = 85) yielded image data that were used to construct B-mode and conventional Nakagami images based on the moment estimator (denoted as mINV images) and maximum-likelihood estimator (denoted as mML images). In addition, novel window-modulated compounding Nakagami images based on the moment estimator (denoted as mWMC images) were also obtained. The means and standard deviations of the Nakagami parameters were examined as a function of the backscattered statistics. The experimental results indicate that the mINV, mML and mWMC images enabled quantitative visualization of the change in backscattered statistics from a Rayleigh distribution to a pre-Rayleigh distribution. Importantly, the mWMC image is superior to both mINV and mML images because it simultaneously realizes sensitive detection of the backscattered statistics and a reduction of estimation variance for image smoothness improvement. We therefore recommend using mWMC image as a novel strategy in Nakagami imaging technique for liver tissue characterization.

Keywords: Envelope statistic; Liver fibrosis; Maximum likelihood estimation; Nakagami imaging.