Imaging in random media with convex optimization

TL;DR

This paper develops a convex optimization-enhanced imaging method for localizing wave sources in random scattering media, effectively mitigating scattering effects and improving source resolution and intensity estimation.

Contribution

It introduces a convex ($l_1$) optimization approach combined with CINT imaging to enhance source localization in scattering media, with theoretical analysis and numerical validation.

Findings

The method improves source localization accuracy in scattering environments.

Convex optimization enhances quantitative source intensity estimates.

Theoretical predictions match numerical simulation results.

Abstract

We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the measurements are affected by cumulative scattering in the medium, but they are not further than a transport mean free path, which is the length scale characteristic of the onset of wave diffusion that prohibits coherent imaging. The inversion is based on the Coherent Interferometric (CINT) imaging method which mitigates the scattering effects by introducing an appropriate smoothing operation in the image formation. This smoothing stabilizes statistically the images, at the expense of their resolution. We complement the CINT method with a convex ($l_1$) optimization in order to improve the source localization and obtain quantitative estimates of the source intensities. We analyze the method in a regime where scattering can be modeled by large random wavefront distortions, and quantify the accuracy of the inversion in terms of the spatial separation of individual sources or clusters of sources. The theoretical predictions are demonstrated with numerical simulations.