THE COMBINED EFFECT OF SIGNAL DECORRELATION AND RANDOM NOISE ON THE VARIANCE OF TIME-DELAY ESTIMATION

Tissue motion and elasticity imaging techniques commonly use time dela y estimation (TDE) for the assessment of tissue displacement. The perf ormance of these techniques is limited because the signals are corrupt ed by various factors including electronic noise, quantisation, and sp eckle decorrelation. Speckle decorrelation is caused by changes in the coherent interference among scatterers when the tissue moves relative to the ultrasound beam. In time delay estimation, the effect of noise is usually addressed through the signal-to-noise ratio (SNR) term. De correlation, often a significant source of error in medical ultrasound , is commonly described in terms of the correlation coefficient. A rel ationship between the correlation coefficient and the SNR was previous ly derived in the literature [1], for identical signals corrupted by u ncorrelated random noise. In this paper, we derive the relationship be tween the peak of the correlation coefficient function and the SNR for two jointly stationary signals when a delay is present between the si gnals. Recently, an expression for the Cramer-Rao lower bound (CRLB) h as been derived in the literature for partially decorrelated signals i n terms of the SNR and the correlation coefficient [2]. Since the appl icability of the CRLB is determined not only by the SNR, but also by t he correlation coefficient, it is important to unify the expression fo r the CRLB for partially correlated signals. In this paper, we derive an expression for the CRLB in term of an equivalent SNR converted from the correlation coefficient using an SNR-rho relationship, and show t his expression to be equivalent to the expression for CRLB in [2]. We also corroborate the validity of the SNR-rho expression with a simulat ion. Using this formulation, correlation measurements can be converted to SNR to obtain a composite SNR. The use of this composite SNR in li eu of those in the CRLB expression in the literature allows the extens ion of the literature results to the solution of the common TDE proble ms that involve signal decorrelation.