Non-linear waveform inverse for biomedical ultrasound imaging

We are looking for a student with a strong background in (applied) mathematics, PDEs, and numerical analysis.

Project description

Wave-based imaging modalities such as biomedical ultrasound (US) are based on sending waves into a medium of interest through its boundary. The wave fields interact with the medium’s internal structures through different wave-matter interactions, e.g., reflection, scattering, or absorption. Measurements of the wave fields leaving the medium thus carry information about its internal properties, and waveform inversion methods try to reconstruct those using a numerical wave propagation model.

Typically, wave propagation in these methods is assumed to be governed by linear PDEs. However, in many relevant applications in biomedical ultrasound, nonlinear wave propagation effects play an important role and cannot be neglected.

The project aims to develop a nonlinear wave inversion approach for ultrasonic fields. The method can be used for, e.g., reconstructing material properties of interest, nonlinearities in the model, convolution kernels for nonlocal dissipation, or the boundary excitation/shape.

Supervision & focus areas

Supervisor : Felix Lucka (CWI), Vanja Nikolic (Radboud University)

Keywords : numerical methods for PDEs, inverse problems, ultrasound imaging