On-shell compression and reconstruction (OSCAR) of monochromatic 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 volume of 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, a physics-based lossy compression scheme for monochromatic wave fields in 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, and a property of every disorder realization rather than of the ensemble average, so that one mask serves an entire ensemble. 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, demonstrated here on sensitivity maps, can be computed via convolution entirely in compressed space while preserving the interference effects. We validate the method in 2D scalar and 3D vector simulations of electromagnetic waves, spanning quasi-ballistic to diffusive transport. The reconstruction error is set by the discarded spectral weight. Demonstrated compression ratios reach ~810x in 2D and ~420x in 3D at a 3% error, with cell-averaged second-order observables accurate to an even smaller error. Tested from quasi-ballistic to diffusive transport, OSCAR stores the fields in up to 19x less space at a 2.5-4.2x lower runtime cost than SZ3. This lowers the storage barrier to ensemble studies at scales relevant to biomedical optics, seismology, and underwater acoustics.