Statistical Analysis of Ultrasound Echo Envelope

Vinayak Dutt, Ph.D. August 1995


The ultrasound echo signal has a statistical nature because it is formed by summation of signals from randomly backscattering sites located randomly inside the medium being imaged. Therefore, the statistics of ultrasound echo signals should be useful for understanding the relationship between the medium parameters and the echo images, and thus for characterization of the scattering media. This thesis focuses on first order statistical analysis for general echo scattering situations. The Rayleigh distribution and its generalized forms, the K and Rice distributions, have been previously suggested to model the echo envelope signal. But these distributions have a very limited applicability. This thesis examines the K distribution and its more generalized version, the homodyned K distribution, which combines the K and Rice distribution features, to model and analyze the statistics of the echo envelope. The analysis shows that the K distribution can be used to model the variations in the statistics of the echo envelope due to variations in the scatterer number density. Also, the signal to noise ratio, SNR, is evaluated for its statistical properties and as a measure of scatterer density. This enables the use of signal-to-noise ratio (SNR) to be used as a statistical parameter for scatterer number density measurement. Also derived is an adaptive filter for speckle reduction based on the K distribution model using this model to quantitate the extent of speckle formation. One of the problems with the statistical analysis is the non-linear signal processing involved in clinical echo imaging systems which changes the statistics of the images acquired from clinical systems. This thesis also examines the log compression involved in the signal processing step of clinical systems and develops the statistics of such compressed images. This analysis shows that the variance of compressed images is a function of the scatterer density. This result could be used to design another speckle reduction filter which can filter the compressed clinical images without having to decompress the images first. Then the more general (and complex) model, the homodyned K distribution model, is examined for modeling any arbitrary backscattered echo signal. This model includes the possibility of a coherent component in the signal and thus is the most general model for the echo envelope. This model provides two parameters, k (the ratio of coherent signal to diffuse signal) and b (which characterizes the clustering of scatterers in the medium), which are useful for general media characterization. The model is used experimentally (and in simulations) to demonstrate the parameterization of scattering media. Various inversion techniques to solve for the parameters using the moments of the distribution are tested for efficacy.

Key words:

  • Echo envelope statistics modeling;
  • K distribution;
  • speckle reduction filtering;
  • SNR imaging;
  • homodyned K distribution