Statistical analysis of strain images estimated from overlapped and filtered echo signals

The visibility of soft-tissue lesions in strain imaging is currently limited by strain noise from waveform decorrelation. Attempts to balance noise reduction with concerns for contrast and spatial resolution rely on accurate models of time delay covariance for guidance. The most useful analytical models describe the covariance of time-varying time delay estimates in terms of experimental parameters and tissue deformation patterns. Assuming compressed tissue deforms linearly along the axis of the sound beam, we derived a delay covariance expression for echo data with Gaussian spectra that were filtered by a Gaussian window function before correlation. The Gaussian filter reduced the number of assumptions needed to obtain closed-form expressions and minimized the effects of strain within the correlation window. However, strain images are often made using uniformly weighted (sinc filtered) window functions. This paper compares time delay covariances for these two window functions, and describes an equivalent window duration at which delay variances for Gaussian and uniform windows are equal. At the equivalent window length, the analysis can be used to predict strain errors for either window function. Finally, this paper uses the delay covariance data to show how strain noise and image sharpness vary depending on the amount of overlap between correlation windows. For an applied strain less than 5%, an overlap near 50% offers an adequate compromise. These results can guide the selection of experimental parameters for improving the visibility of lesions in strain images.