Anthony L. Gerig

Statistics of ultrasonic scatterer size estimation with a reference phantom

A theoretical expression for the variance of scatterer size estimates is derived for a modified least squares size estimator used in conjunction with a reference phantom method for backscatter coefficient measurement. A Gaussian spatial autocorrelation function is assumed. Simulations and phantom experiments were performed to verify the results for backscatter and size variances. The dependence of size estimate errors upon free experimental parameters is explored. Implications of the findings for the optimization of scatterer size estimation are discussed. The utility of scatterer size parametric imaging is examined through the signal to noise ratio comparison with standard ultrasonic B-mode imaging.

Improved parametric imaging of scatterer size estimates using angular compounding

The feasibility of estimating and imaging scatterer size using backscattered ultrasound signals and spectral analysis techniques was demonstrated previously. In many cases, size estimation, although computationally intensive, has proven to be useful for monitoring, diagnosing, and studying disease. However, a difficulty that is encountered in imaging scatterer size is the large estimator variance caused by statistical fluctuations in echo signals from random media. This paper presents an approach for reducing these statistical uncertainties. Multiple scatterer size estimates are generated for each image pixel using data acquired from several different directions. These estimates are subsequently compounded to yield a single estimate that has a reduced variance. In this feasibility study, compounding was achieved by translating a sectored-array transducer in a direction parallel to the acquired image plane. Angular compounding improved the signal-to-noise ratio (SNR) in scatterer size images. The improvement is proportional to the square root of the effective number of statistically independent views available for each image pixel.

Correlation of RF signals during angular compounding

A theoretical analysis of the correlation between radio-frequency (RF) echo signal data acquired from the same location but at different angles is presented. The accuracy of the theoretical results is verified with computer simulations. Refinements to previous analyses of the correlation of RF signals originating from the same spatial location at different angular positions are made. We extend the analysis to study correlation of RF signals coming from different spatial locations and eventually correlation of RF signal segments that intersect at the same spatial location. The theory predicts a faster decorrelation with a change in the insonification angle for longer RF echo signal segments. As the RF signal segment becomes shorter, the decorrelation rate with angle is slower and approaches the limit corresponding to the correlation of RF signals originating from the same spatial location. Theoretical results provide a clear understanding of angular compounding techniques used to improve the signal-to-noise ratio in ultrasonic parametric imaging and in elastography.

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

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.

Spectral and Scatterer-Size Correlation during Angular Compounding: Simulations and Experimental Studies

In a previous study, theoretical expressions were derived for the correlation between ultrasonic scatterer-size estimates and their associated spectral measures when echo data are acquired from the same location but at different angles. The results were verified using simulations. In the present work, we further analyze simulation data for these conditions; in addition, we measure the correlations using a cylindrical tissue-mimicking phantom. Experimental and theoretical results show that the relationship of scatterer-size correlation to insonification angle depends on gate duration, gate type and beam profile. Some discrepancies are noted between experimental results and theoretical predictions, particularly when using smaller gated windows. The sources of the discrepancies are discussed. Experimental results using a 6-MHz linear array suggest that, to save acquisition and processing time while reducing variance, a 2°–3° angular increment step provides efficient angular compounding for scatterer-size imaging with this array. Theoretical predictions can provide estimates of expected correlations between angular acquisitions when compounding with other transducers.

Optimization of angular and frequency compounding in ultrasonic attenuation estimations

Previous reports have shown that the variance in ultrasound attenuation measurements is reduced when spatial and frequency compounding were applied in data acquisition and analysis. This paper investigates factors affecting the efficiency of compound attenuation imaging methods. A theoretical expression is derived that predicts the correlation between attenuation versus frequency slope (beta) estimates as a function of the increment between measurement frequencies (deltaf ) and the angular separation between beam lines (Delta (theta)). Theoretical results are compared with those from attenuation measurements on tissue-mimicking phantoms and from simulation data. Both predictions and measurement results show that the correlation between beta estimates as a function of (Delta f ) is independent of the length of the radio frequency (rf) data segment over which beta is derived. However, it decreases with an increase in the length of the data segment used in power spectra estimates. In contrast, the correlation between beta estimates as a function of delta(theta) decreases when the rf data segment length is longer or the frequency of the signal is higher. O 2005 Acoustical Society of America.

Parametric imaging using a clinical scanner

Ultrasonic scatterer size estimation and imaging has proven to be both feasible and useful for monitoring, diagnosis, and study of disease. We are implementing scatterer size imaging and attenuation coefficient imaging on a clinical scanner equipped with a research interface. The interface provides radio frequency echo data over the image of a sample, which are then analyzed offline. Echo data from a reference phantom, acquired using the same transducer and scanner settings, accounts for system dependencies on the data. Backscatter coefficient and attenuation coefficients are estimated for small regions. Scatterer size images are generated by performing, a modified least squares fit of the backscatter estimate to a theoretical model, which relates backscatter to scatterer size. Tests in well-characterized phantoms to demonstrate the accuracy of the method have revealed limitations. Ultrasonic scatterer size estimates generally have large variances due to the inherent noise of the 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. Initial compound acquisitions on the clinical system have been done using manually generated scripts supported by the research interface. Results confirm theoretical expectations of the improvement in signal-to-noise ratio of scatterer size estimations with selected compounding parameters. Additional parameters, including the attenuation coefficient, may also be derived.

Errors in ultrasonic scatterer size estimates due to phase and amplitude aberration

Current ultrasonic scatterer size estimation methods assume that acoustic propagation is free of distortion due to large-scale variations in medium attenuation and sound speed. However, it has been demonstrated that under certain conditions in medical applications, medium inhomogeneities can cause significant field aberrations that lead to B-mode image artifacts. These same aberrations may be responsible for errors in size estimates and parametric images of scatterer size. This work derives theoretical expressions for the error in backscatter coefficient and size estimates as a function of statistical parameters that quantify phase and amplitude aberration, assuming a Gaussian spatial autocorrelation function. Results exhibit agreement with simulations for the limited region of parameter space considered. For large values of aberration decorrelation lengths relative to aberration standard deviations, phase aberration errors appear to be minimal, while amplitude aberration errors remain significant. Implications of the results for accurate backscatter and size estimation are discussed. In particular, backscatter filters are suggested as a method for error correction. Limitations of the theory are also addressed. The approach, approximations, and assumptions used in the derivation are most appropriate when the aberrating structures are relatively large, and the region containing the inhomogeneities is offset from the insonifying transducer.

Errors in ultrasonic scatterer size estimates due to mixed scatterer populations

Ultrasonic scatterer size estimation provides an accurate measure of actual scatterer size when those sizes are narrowly distributed about a single, mean value. Although often the case, there are instances in tissue where two or more scatterer types with significantly different sizes are believed to contribute to the same signal. The purpose of this work is to characterize the errors in the size estimates obtained for one scatterer type when contaminating scatterers of a second type are present. Theoretical results for the error are compared with simulation and experimental results for uniform phantoms containing a binary mixture of scatterers. These results indicate that errors can be significant for the frequency bands typically used in size estimation, especially when contaminant scatterers are larger than the scatterers of interest. Results also indicate, however, that these errors can be reduced by shifting the frequency band used to estimate size. A technique for correcting the errors is also descri...

Near-specular acoustic scattering from a buried submarine mud volcano.

Submarine mud volcanoes are objects that form on the seafloor due to the emission of gas and fluidized sediment from the Earths interior. They vary widely in size, can be exposed or buried, and are of interest to the underwater acoustics community as potential sources of active sonar clutter. Coincident seismic reflection data and low frequency bistatic scattering data were gathered from one such buried mud volcano located in the Straits of Sicily. The bistatic data were generated using a pulsed piston source and a 64-element horizontal array, both towed over the top of the volcano. The purpose of this work was to appropriately model low frequency scattering from the volcano using the bistatic returns, seismic bathymetry, and knowledge of the general geoacoustic properties of the areas seabed to guide understanding and model development. Ray theory, with some approximations, was used to model acoustic propagation through overlying layers. Due to the volcanos size, scattering was modeled using geometric acoustics and a simple representation of volcano shape. Modeled bistatic data compared relatively well with experimental data, although some features remain unexplained. Results of an inversion for the volcanos reflection coefficient indicate that it may be acoustically softer than expected.