A learned born series for highly scattering media

Abstract

The Helmholtz equation with heterogeneous material properties is essential in various fields requiring single-frequency wave simulations, including optics, seismology, acoustics, and electromagnetics. Traditional methods for solving this equation, such as the Born Series, face limitations in converging for high-contrast scattering potentials. To address this challenge, we introduce a novel method called the Learned Born Series (LBS). The LBS is derived from the convergent Born Series but employs components that are learned through training. It demonstrates significantly improved accuracy compared to the conventional convergent Born Series, especially in scenarios with high-contrast scatterers, while maintaining similar computational complexity. The LBS can rapidly generate reasonably accurate predictions of the global pressure field with only a few iterations, and the errors decrease as more iterations are learned. We show its effectiveness through experiments on simulated datasets. The LBS offers promising prospects for accelerating simulations in scenarios with strong sound speed contrasts, potentially revolutionizing applications in transcranial treatment planning and full waveform inversion.