Nonlinearity Parameter Imaging Using a Multi-View Joint Inverse Problem Formulation

The acoustic nonlinearity parameter (B/A) is a promising biomarker for diagnosing conditions like nonalcoholic fatty liver disease (NAFLD). The estimation of the B/A can be performed using the depletion method, which constructs a parametric map by solving an inverse problem based on measurements from pulse-echo acquisitions at quasi-linear and nonlinear ultrasound pressure levels. Solving the inverse problem combined with the total variation regularization (TVR) decreases the large variance of the B/A estimates at the expense of increased bias. To improve the trade-off between bias and variance, a recent depletion method spatial compounding (DeSC) framework was developed, however, it is still limited by oversmoothing, which leads to loss of spatial resolution. In the present work, a depletion method multi-view spatial compounding (DeMuSC) that formulates the local B/A estimation as a joint inverse problem is proposed. This approach integrates measurements acquired at multiple steering angles into a single overdetermined linear system. By directly exploiting angular information in a single inverse problem rather than averaging several parametric images, the proposed method improves the bias-variance trade-off while preserving spatial detail. Simulation results validate this approach. The DeMuSC reduces the estimation standard deviation by approximately 54% compared to DeSC without TVR. Considering TVR, the DeMuSC nearly doubles the lateral (2.39 mm vs. 6.67 mm) and axial resolution (3.61 mm vs. 7.49 mm).