A direct comparison of time reversal and cross correlation for shear wave elastography

This work presents a direct comparison of time reversal (TR) and cross correlation (CC) for wave refocusing, with application to shear wave elastography. Standard theoretical equivalence relies on idealized assumptions, such as diffuse fields, that are rarely met in practice. A unified framework based on a reciprocal configuration to enable a direct, assumption-free comparison is proposed. A key distinction is drawn between active TR, requiring separate forward and backward wavefield acquisitions, and passive TR, computed from a single forward acquisition. It is demonstrated that TR and CC are two sides of the same refocusing process, connected through a decomposition of the CC field into diagonal and off diagonal (OD) components. The performance of passive CC is governed by the source characteristics: for impulsive sources, refocusing is maximized when the inter-source delay exceeds the signal duration, suppressing OD interference; for continuous noise, performance is limited by the noise autocorrelation. It is validated that high-fidelity shear wave speed maps can be reconstructed via direct wave inversion from TR and CC focusing fields, with a maximum difference of 4%, confirming that equivalent mechanical information is extracted.