Analytical phase tracking based strain estimation

A new strain estimator for quasi-static elastography is presented, based on tracking of the analytical signal phase as a function of the external force. Two implementations are introduced: zero-phase search with moving window (SMW) and zero-phase band tracking using connected component labeling (CCL). Low analytical signal amplitude caused by local destructive interference is associated with large error in the phase trajectories, and amplitude thresholding can thus be used to terminate the phase tracking along a particular path. Interpolation is then applied to estimate displacement in the eliminated path.

The paper describes first a mathematical analysis based on 1-D multi-scatter modeling, followed by a statistical study of the displacement and strain error. Simulation and experiment with an inhomogeneous phantom indicate that SMW and CCL are capable of reliably estimating tissue displacement and strain over a larger range of deformation than standard timedomain cross-correlation (SCC). Results also show that SMW is roughly 40 times faster than SCC with comparable or even better accuracy. CCL is slower than SMW, but more noise robust. Simulation assessment at compression level 3% and 6% with SNR 20 dB demonstrates average strain error for SMW and CCL of 10%, whereas SCC achieves 18%.