Speaker
Description
The inverse acoustic scattering problem refers to the mathematical imaging problem of reconstructing the speed of sound in a medium from a collection of scattered waves. A popular approach is full waveform inversion, which addresses this non-linear inverse problem iteratively without simplifying the underlying mathematical model leading to highly accurate solutions at the expense of increased computational effort.
Diffraction tomography (DT) provides an alternative approach by linearizing the inverse problem under the first Born approximation, enabling efficient computations and hence potential application in medical ultrasound imaging. However, in conventional DT, the incident wave is assumed to be a monochromatic plane wave. This is an unrealistic simplification in medical ultrasound imaging where a transducer typically emits focused beams to a region of interest in the human body.
In this talk, we extend conventional DT by introducing the concept of Gaussian fields of incidence. Herewith, focused beams are modeled, allowing customization by adjusting the beam waist and focal depth. We present a new forward model that incorporates a Gaussian field of incidence and extends the classical Fourier diffraction theorem to the use of this incident field. This focused illumination approach enables new measurement geometries for data generation, based on which we develop reconstruction methods. These are then comprehensively evaluated through numerical experiments.
