Implementation and Validation of the Multi-scale Gradient Smoothing Strategy for Breast Full Waveform Inversion

Full waveform inversion (FWI) is an advanced technique for reconstructing high-resolution sound speed images, offering quantitative measurements of tissue sound speed in ultrasound computed tomography. However, FWI is susceptible to the issue of cycle skipping, which frequently causes the inversion to converge to a local minimum. To help mitigate cycle skipping, this paper proposes a modified FWI algorithm.

Our approach incorporated low-wavenumber extraction in the image domain, capitalizing on the inherent large-scale background information in the gradient. Within a Gaussian gradient filtering (GGF) framework, we extract a robust low-wavenumber gradient-referred to as gradient smoothing-to drive stable updates and we extend this into a multi-scale GGF strategy by progressively reducing the standard deviation of the low-pass filter over the inversion.

A comparative analysis between the proposed method and conventional FWI was conducted in numerical experiments. Compared with conventional FWI, the GGF + FWI reduced the sound-speed reconstruction root mean square error and improved the structural similarity index measure. In vivo breast experiments confirmed the robustness of our method. In the comparison of FWI, frequency-shifted envelope-based global correlation norm, frequency-shifted envelope-based global correlation norm + FWI and multi-scale GGF, the effectiveness of multi-scale GGF was confirmed by the highest contrast-to-noise ratio.

These results demonstrate that the proposed approach can improve the convergence properties of the optimization algorithm and mitigate artefacts.