ERROR ANALYSIS IN ACOUSTIC ELASTOGRAPHY .1. DISPLACEMENT ESTIMATION

Correlation between acoustic echo signals obtained before and after ap plication of an external compressional force provides information abou t the internal deformation of an elastic medium. In this paper, the va riance for displacement estimated from an echo data segment and the co variance between two windowed segments that may overlap are derived. T he signal and noise spectra are Gaussian and independent. The dependen ce of the displacement variance on input signal-to-noise ratio (SNR,), time-bandwidth product W, fractional bandwidth Y-1, and the rate of d isplacement variation with depth a is investigated. The relationship b etween a and the other experimental parameters is crucial for understa nding how signal decorrelation affects displacement error. The express ion for displacement variance reduces to the Cramer-Rao lower bound re sult when a = 0 and W much greater than 1 for both bandpass and base-b and signals. When a not equal 0 displacement variance increases, and t here is an optimal window length at W = root 20/a root 1+Y-2 for which the displacement variance is minimum. Narrow-band signals produce lar ger errors than broadband signals for long observation windows when a not equal 0 and just the opposite when a=0. Errors are greatest for di splacements estimated from the envelope of narrow-band signals. Finall y, a general expression for the minimum displacement variance for arbi trary signal and noise spectra is derived as a function of the experim ental parameters. These results form a framework for analyzing strain estimates in elastography, the subject of a companion paper. (C) 1997 Acoustical Society of America.