Estimating the elastographic signal-to-noise ratio using correlation coefficients

In conventional elastography, strain is estimated from the gradient of the displacement (time-delay) estimates. The displacement estimates involve estimating the peak location of the cross-correlation function between matching pre- and post-compression A-lines. Bias errors in estimating the peak location of the cross-correlation function, amplified by the gradient operation on the displacement estimates (needed for the computation of the strain), could result in values of elastographic signal-to-noise ratio (SNR(e)) that exceed the theoretical upper bounds, thereby hindering a consistent interpretation of this parameter. These algorithmic errors have not been accounted for by the theory. We propose the use of the measured correlation coefficients in the theoretical SNR(e) expressions to estimate the SNR(e), rather than computing them directly from the elastograms. This methodology results in values of SNR(e) that are lower than the theoretical upper bounds, thereby avoiding the problems associated with computing SNR(e) directly from the elastograms. Using simulated models of uniformly elastic phantoms, a proof of principle of such an SNR(e) measure is shown.