Regularization for ultrasonic measurements of tissue displacement vector and strain tensor

In this report, we present the regularization results of displacement vector measurement by the multidimensional cross-spectrum phase gradient method (MCSPGM), multidimensional autocorrelation method (MAM), and multidimensional Doppler method (MDM) without lateral modulation. In addition to the results of spatially variant regularization in displacement vector measurement using displacement variances, the results of displacement component-dependent regularization are presented. That is, according to the measurement accuracy of displacement components, the regularization is properly applied to the respective displacement components. For instance, only the regularization on the lateral displacement is effective. That is, for the lateral nonmodulation case, the accuracies and stabilities of lateral/elevational displacement measurements significantly increase. In conjunction, the convergence speed of phase matching also increases. The demonstrated measurements of the displacement vector distributions in experiments using inhomogeneous shear modulus agar phantoms confirm that displacement-componentdependent regularization enables better strain tensor measurement and shear modulus reconstruction from the viewpoints of accuracy and stability. The contrast-to-noise ratio (CNR) is useful to set regularization parameters properly for the displacement regularization, whereas the CNR is useless for shear modulus regularization in the sense that the accuracy of reconstruction value cannot be evaluated.