New phase-matching method for ultrasonic tissue displacement and strain measurements: Application of maximum likelihood and maximum a posteriori estimations to multidimensional autocorrelation method

To directly perform new maximum likelihood (ML) and maximum a posteriori (MAP) estimations with respect to ultrasonic human tissue Doppler equations expressed for a target displacement, the author's previously developed rf-echo phase-matching method is modified. Instead of coarse and residual displacement estimates successively obtained with the multidimensional cross-correlation and autocorrelation methods, respectively, an addition is equivalently performed with respect to the phase differences corresponding to the coarse and residual estimates. The feasibility of this method is verified through experiments using an agar phantom having a high-shear-modulus inclusion compressed laterally. The MAP estimation yields more accurate and stable results than the ML estimation for all three system conditions considered, i.e., a well-conditioned case with a regular lateral modulation, a slightly ill-conditioned overdetermined (OD) case inherent to the use of plurally steered beams, and a completely ill-conditioned OD case inherent to quasi-waves with low independence generated by spectral frequency division from single-beam-scanned echo data.