Quantification of limitations in statistical analysis of ultrasound echo envelope amplitudes

Abstract Ultrasound echo envelope statistics have been widely studied for quantitative tissue characterization. In ultrasound measurements, the size of the region-of-interest (ROI) is limited by several factors, such as the locality of the tissue characteristics and the depth dependence of the acoustic field of the ultrasound beam. In this case, the evaluated echo envelope statistics vary even when the envelope amplitudes follow the same population without any noise. In this study, the statistical variance of the moments caused by this finite number of samples was quantified based on the central limit theorem and the law of error propagation. The proposed principles were validated by random number simulation and used to quantify the statistical variance of Nakagami parameter estimation. Finally, the effective number of independent samples in an ultrasonic measurement was quantified based on the relationship between the ROI size and the ultrasound spatial resolution.