Correlation of ultrasonic scatterer size estimates for the statistical analysis and optimization of angular compounding

Abstract

Ultrasonic scatterer size estimates generally have large variances due to the inherent noise of spectral estimates used to calculate size. Compounding partially correlated size estimates associated with the same tissue, but produced with data acquired from different angles of incidence, is an effective way to reduce the variance without making dramatic sacrifices in spatial resolution. This work derives theoretical approximations for the correlation between these size estimates, and the coherence between their associated spectral estimates, as functions of ultrasonic system parameters. A Gaussian spatial autocorrelation function is assumed to adequately model scatterer shape. Both approximations compare favorably with simulation results, which consider validation near the focus. Utilization of the correlation/coherence expressions for statistical analysis and optimization is discussed. Approximations, such as the invariance of phase and amplitude terms with angle, are made to obtain closed-form solutions to the derived spectral coherence near the focus and permit analytical optimization analysis. Results indicate that recommended parameter adjustments for performance improvement generally depend upon whether, for the system under consideration, the primary source of change in total coherence with rotation is phase term variation due to the change in the relative position of scattering sites, or field amplitude term variation due to beam movement.

2G-5 Methods for Improvement on Liver Scatterer Size Estimates

“…This is because compounding of uncorrelated data is most efficient. We have derived a theoretical expression for the correlation between scatterer size estimates during angular compounding [5]. Here we show more recent studies where the theoretical expressions are verified by experiments.…”

Improvements in elastographic contrast-to-noise ratio using spatial-angular compounding

“…Spatial angular compounding of other parametric images of ultrasonic tissue characterization parameters such as scatterer size (Gerig et al 2004a(Gerig et al , 2004b) and attenuation coefficient estimates (Tu et al 2003) have also been shown to significantly reduce estimation noise. In addition, for elastographic applications, angular insonifications have also been utilized to image tissue displacement information in 2-D, thereby enabling estimation of both the normal and shear strain components, without assuming tissue incompressibility (Techavipoo et al 2004a).…”

Improving the Statistics of Quantitative Ultrasound Techniques with Deformation Compounding: An Experimental Study

“…The methods proposed here are conceptually similar to those used in the ultrasound spatial compounding literature (Trahey et al, 1986; O’Donnell and Silverstein, 1988; Li and O’Donnell, 1994; Gerig et al, 2004a) where spatial translations or rotations of an object being imaged have been used to change the scatterer distribution, z ( x, t ), as viewed by the interrogating pulse, in an effort to sufficiently decorrelate the signal allowing independent realizations of echo signal data to be averaged. However, as an alternative approach in this study, we attempted to slightly deform the tissue to spatially redistribute these scatterers in order to obtain more independent realizations of the echo signal from a medium containing randomly positioned scatterers.…”