Detecting changes in ultrasound backscattered statistics by using Nakagami parameters: Comparisons of moment-based and maximum likelihood estimators.

The Nakagami distribution is an approximation useful to the statistics of ultrasound backscattered signals for tissue characterization. Various estimators may affect the Nakagami parameter in the detection of changes in backscattered statistics. In particular, the moment-based estimator (MBE) and maximum likelihood estimator (MLE) are two primary methods used to estimate the Nakagami parameters of ultrasound signals. This study explored the effects of the MBE and different MLE approximations on Nakagami parameter estimations. Ultrasound backscattered signals of different scatterer number densities were generated using a simulation model, and phantom experiments and measurements of human liver tissues were also conducted to acquire real backscattered echoes. Envelope signals were employed to estimate the Nakagami parameters by using the MBE, first- and second-order approximations of MLE (MLE and MLE, respectively), and Greenwood approximation (MLE) for comparisons. The simulation results demonstrated that, compared with the MBE and MLE, the MLE and MLE enabled more stable parameter estimations with small sample sizes. Notably, the required data length of the envelope signal was 3.6 times the pulse length. The phantom and tissue measurement results also showed that the Nakagami parameters estimated using the MLE and MLE could simultaneously differentiate various scatterer concentrations with lower standard deviations and reliably reflect physical meanings associated with the backscattered statistics. Therefore, the MLE and MLE are suggested as estimators for the development of Nakagami-based methodologies for ultrasound tissue characterization.