LAUSR

A coupled computational method for recovering tissue velocity vector fields from high-frame-rate echocardiography is described. Conventional transthoracic echocardiography provides limited temporal resolution, which may prevent accurate estimation of the 2-D myocardial velocity field dynamics. High-frame-rate compound echocardiography using diverging waves with integrated motion compensation has been shown to provide concurrent high-resolution B-mode and tissue Doppler imaging (TDI). In this paper, we propose a regularized least-squares method to provide accurate myocardial velocities at high frame rates. The velocity vector field was formulated as the minimizer of a cost function that is a weighted sum of: 1) the ${\ell }^{{2}}$ -norm of the material derivative of the B-mode images (optical flow); 2) the ${\ell }^{{2}}$ -norm of the tissue-Doppler residuals; and 3) a quadratic regularizer that imposes spatial smoothness and well-posedness. A finite difference discretization of the continuous problem was adopted, leading to a sparse linear system. The proposed framework was validated in vitro on a rotating disk with speeds up to 20 cm/s, and compared with speckle tracking echocardiography (STE) by block matching. It was also validated in vivo against TDI and STE in a cross-validation strategy involving parasternal long axis and apical three-chamber views. The proposed method based on the combination of optical flow and tissue Doppler led to more accurate time-resolved velocity vector fields.