ALTRUIST: Alternating Direction Method of Multipliers for Total Variation Regularization in Ultrasound Strain Imaging

Ultrasound strain imaging, which delineates mechanical properties to detect tissue abnormalities, involves estimating the time-delay between two radio-frequency (RF) frames collected before and after tissue deformation. The existing regularized optimization-based time-delay estimation (TDE) techniques suffer from at least one of the following drawbacks: 1) The regularizer is not aligned with tissue deformation physics due to taking only the first-order displacement derivative into account. 2) The L2-norm of the displacement derivatives, which oversmoothes the estimated time-delay, is utilized as the regularizer. 3) The absolute value function’s sharp corner should be approximated by a smooth function to facilitate the optimization of L1-norm. Herein, to resolve these shortcomings, we propose employing the alternating direction method of multipliers (ADMM) for optimizing a novel cost function consisting of L2norm data fidelity term, L1-norm firstand second-order spatial continuity terms. ADMM empowers the proposed algorithm to use different techniques for optimizing different parts of the cost function and obtain high-contrast strain images with smooth background and sharp boundaries. We name our technique ADMM for totaL variaTion RegUlarIzation in ultrasound STrain imaging (ALTRUIST). In extensive simulation, phantom, and in vivo experiments, ALTRUIST substantially outperforms GLUE, OVERWIND, and L1-SOUL, three recently-published TDE algorithms, both qualitatively and quantitatively. ALTRUIST yields 89%, 88%, and 26% improvements of contrast-to-noise ratio over L1-SOUL for simulated, phantom, and in vivo liver cancer datasets, respectively. We will publish the ALTRUIST code after the acceptance of this paper at http://code.sonography.ai.