Ultrasound Autofocusing: Common Midpoint Phase Error Optimization via Differentiable Beamforming

Abstract: Wavefield imaging reconstructs physical properties from wavefield measurements across an aperture, using modalities like radar, optics, sonar, seismic, and ultrasound imaging. Propagation of a wavefront from unknown sources through heterogeneous media causes phase aberrations that degrade the coherence of the wavefront leading to reduced image resolution and contrast. Adaptive imaging techniques attempt to correct phase aberration and restore coherence leading to improved focus. We propose an autofocusing paradigm for aberration correction in ultrasound imaging by fitting an acoustic velocity field to pressure measurements, via optimization of the common midpoint phase error (CMPE), using a straight-ray wave propagation model for beamforming in diffusely scattering media. We show that CMPE induced by heterogeneous acoustic velocity is a robust measure of phase aberration that can be used for acoustic autofocusing. CMPE is optimized iteratively using a differentiable beamforming approach to simultaneously improve the image focus while estimating the acoustic velocity field of the interrogated medium. The approach relies solely on wavefield measurements using a straight-ray integral solution of the two-way time-of-flight without explicit numerical time-stepping models of wave propagation. We demonstrate method performance through in silico simulations, in vitro phantom measurements, and in vivo mammalian models, showing practical applications in distributed aberration quantification, correction, and velocity estimation for medical ultrasound autofocusing.