Momentum equation-based regularization and image registration for two-dimensional ultrasound elasticity imaging

The objective of this paper is to evaluate and compare multiple mechanics-based and traditional regularization strategies within a variational image registration framework for quasi-static ultrasound elastography. We reformulate a previously proposed momentum-equation-based post-processing method (SPREME) as a regularization term directly integrated into an image registration energy functional. Four regularization types are implemented and compared: a strain magnitude ([Formula: see text]), a strain magnitude with incompressibility constraint ([Formula: see text]), and a momentum-based regularization under plane strain ([Formula: see text]) and plane stress ([Formula: see text]) assumptions. Registration performance is assessed using synthetic ultrasound image sequences generated from 2D and 3D finite element simulations, as well as experimental phantom data, and displacement and strain field errors, strain contrast, and contrast-to-noise ratio are compared. Momentum-based regularization that incorporates momentum conservation outperforms strain-based techniques in elastographic image registration, particularly when applied directly in the optimization framework. This approach improves robustness to noise and model mismatch, offering a promising direction for future displacement-based inverse imaging methods.