An Improved Parameter Estimator of the Homodyned K Distribution Based on the Maximum Likelihood Method for Ultrasound Tissue Characterization

Abstract

The homodyned K distribution (HK) can generally describe the ultrasound backscatter envelope statistics distribution with parameters that have specific physical meaning. However, creating robust and reliable HK parameter estimates remains a crucial concern. The maximum likelihood estimator (MLE) usually yields a small variance and bias in parameter estimation. Thus, two recent studies have attempted to use MLE for parameter estimation of HK distribution. However, some of the statements in these studies are not fully justified and they may hinder the application of parameter estimation of HK distribution based on MLE. In this study, we propose a new parameter estimator for the HK distribution based on the MLE (i.e., MLE1), which overcomes the disadvantages of conventional MLE of HK distribution. The MLE1 was compared with other estimators, such as XU estimator (an estimation method based on the first moment of the intensity and tow log-moments) and ANN estimator (an estimation method based on artificial neural networks). We showed that the estimations of parameters α and k are the best overall (in terms of the relative bias, normalized standard deviation, and relative root mean squared errors) using the proposed MLE1 compared with the others based on the simulated data when the sample size was N = 1000. Moreover, we assessed the usefulness of the proposed MLE1 when the number of scatterers per resolution cell was high (i.e., α up to 80) and when the sample size was small (i.e., N = 100), and we found a satisfactory result. Tests on simulated ultrasound images based on Field II were performed and the results confirmed that the proposed MLE1 is feasible and reliable for the parameter estimation from the ultrasonic envelope signal. Therefore, the proposed MLE1 can accurately estimate the HK parameters with lower uncertainty, which presents a potential practical value for further ultrasonic applications.

In Situ Monitoring and Assessment of Ischemic Skin Flap by High-Frequency Ultrasound and Quantitative Parameters

“…On the other hand, the resultant echoes are also largely affected by acoustical properties and the arrangement of scatterers in the interrogated medium [ 18 , 22 ]. Consequently, a statistical approach by estimating the parameters of statistical models, such as Rician, K, homodyned K, and generalized K distributions [ 23 , 24 ], becomes feasible for adoption in differentiating different scattering signals of random nature processes. Specifically, statistical parameters are estimated from the probability density function (PDF) of ultrasonic backscattered envelopes, and may correlate with the concentration and arrangement of scatterers.…”

Ultrasound Entropy Imaging Based on the Kernel Density Estimation: A New Approach to Hepatic Steatosis Characterization

“…These techniques can be classified into model-based and non-model-based ones. Typical model-based techniques are ultrasound Nakagami imaging [10][11][12][13] and homodyned-K imaging [14,15] that are based on the generalized statistical models of backscatter envelopes. Ultrasound entropy imaging uses the informationtheoretic entropy of ultrasound backscatter envelopes, without a perquisite for satisfying a specific statistical model [9], which is of growing research interest in the field of quantitative ultrasound.…”