Universal compression of wave fields in weakly scattering media

Abstract

Advances in computational methods have made full-wave simulations in large disordered media increasingly feasible, but the resulting field data, scaling with the cube of the ratio of system size to wavelength, creates a severe storage and post-processing bottleneck. Generic compression methods are sample-specific and preclude operations on compressed data. We introduce OSCAR (On-Shell Compression And Reconstruction), a physics-based lossy compression scheme for weakly scattering media. OSCAR exploits the universal confinement of the Fourier representation of wave fields to a thin dispersion shell, a direct consequence of wave propagation when the scattering mean free path significantly exceeds the wavelength. The resulting compression ratio reflects two distinct scale separations: on-shell confinement due to weak scattering, and the excess Fourier-space volume introduced by sub-wavelength discretization of the scatterers. Crucially, second-order quantities such as intensity, correlations, and (optical) sensitivity can be computed via convolution entirely in compressed space and remain accurate even when individual field reconstruction incurs appreciable error, because coherent interference between independently compressed fields is preserved. Numerical simulations of electromagnetic waves in 2D and 3D confirm compression ratios up to ${\sim}380\times$ with sub-percent field error, enabling routine ensemble studies at scales relevant to biomedical optics, seismology, and underwater acoustics.