Full-Waveform Inversion for Breast Ultrasound Tomography Using Line-Shape Modeled Elements

The objective of the work described here was to incorporate the spatial shapes of the transducer elements into the framework of the full-waveform inversion.

An element is treated as its cross-section in the 2-D imaging plane, that is, a line segment. The elements are not simply modeled as a set of point sources on their surface to avoid staircasing artifacts. By use of the Fourier collocation method, an element is spatially represented as the discrete convolution between its spatial distribution and a band-limited delta function. The excitation pulses on the emitters and recorded signals on the receivers are then weighted based on the discrete convolution results. Digital and physical experiments are implemented to validate the method.

It is meaningful to model the shapes of the elements if their spatial sizes are similar to or larger than the acoustic wavelengths. It should, however, be noted that because this article focuses on 2-D imaging, the inter-plane effects are not considered.

The approach helps reduce the root mean square errors and increase the structural similarity of the reconstructed images. It also helps to improve the stability of convergence and to accelerate the convergence speed.