Regularized Joint Estimator of the Nonlinearity Parameter and Attenuation Coefficient Using a Nonlinear Least-Squares Algorithm

The acoustic nonlinearity parameter (B/A) could enhance the diagnostic capabilities of conventional ultrasonography and quantitative ultrasound in tissues and diseases. Nonlinear acoustic propagation theory of plane waves has been used to develop a dual-energy model of the depletion of the fundamental related to the Gol’dberg number and subsequently to the B/A of media (a reference phantom is used as a baseline). The depletion method, however, needs a priori information of the attenuation coefficient (AC) of the assessed media. For this reason, recently, a work introduced a simultaneous estimator of the B/A and AC based on fitting depletion method measurements to a nonlinear model using the iterative algorithm Gauss-Newton Levenberg-Marquardt (GNLM). However, the GNLM method presented high sensitivity to the initial guess values of the algorithm which limits the robustness of the approach. In the present work, the Gauss-Newton method is combined with a total variation regularization approach (GNTV), which is achievable by expanding the nonlinear model of the GNLM method for joint estimation of the B/A and AC of all pixels of the parametric images instead of a block-wise approach. In addition, the GNTV used compounding data from several tone-burst transmissions at different center frequencies rather than only one narrowband tone-burst. The results suggest that incorporating regularization and increasing the number of frequencies improves the robustness of the GNTV compared to the GNLM method by accurately estimating B/A values in uniform and nonuniform experimental phantoms (mean relative error less than 18%). The best performance of B/A reconstruction was observed when the sample medium exhibited a constant Gol’dberg number.