Physics-Constrained Regularization for Robust Ultrasound Thermal Displacement Estimation

Robust displacement estimation is crucial for ultrasound thermal strain imaging (TSI), but is severely hampered by noise and the thermal-acoustic lens (TALs) effect. This article introduces NLOG, a displacement estimator that builds upon the NL (NXcorr + Loupas) method and incorporates a physics-based Gaussian thermal strain prior within a global optimization framework to overcome the limitations of conventional window-based methods. Specifically, after an initial displacement field is obtained using the conventional NL estimator, a Gaussian strain prior is extracted and used to regularize a global cost function, yielding a physically plausible displacement field. Validated via simulations (with ground truth) and ex vivo experiments, NLOG significantly suppresses noise and artifacts, improving strain image quality, with average gains in strain signal-to-noise ratio (SNR) and contrast-to-noise ratio of over 200% in simulations and 300% in experiments compared to the baseline method. Consequently, temperature estimation errors are reduced by more than 36%. The proposed estimator may therefore contribute to safer and more effective clinical thermal therapies by enabling real-time, artifact-robust temperature monitoring during focused ultrasound (FU) treatment.