A quadratic energy minimization framework for signal loss estimation from arbitrarily sampled ultrasound data

We present a flexible and general framework to iteratively solve quadratic energy problems on a non uniform grid, targeted at ultrasound imaging. Therefore, we model input samples as the nodes of an irregular directed graph, and define energies according to the application by setting weights to the edges. To solve the energy, we derive an effective optimization scheme, which avoids both the explicit computation of a linear system, as well as the compounding of the input data on a regular grid. The framework is validated in the context of 3D ultrasound signal loss estimation with the goal of providing an uncertainty estimate for each 3D data sample. Qualitative and quantitative results for 5 subjects and two target regions, namely US of the bone and the carotid artery, show the benefits of our approach, yielding continuous loss estimates.