Imaging in random media with convex optimization
For researchers in wave imaging and inverse problems, this work provides a method to enhance source localization in random media beyond the transport mean free path, though it is an incremental improvement over existing CINT methods.
This paper addresses the inverse problem of localizing wave sources in random scattering media from time-resolved measurements. By combining Coherent Interferometric (CINT) imaging with convex l1 optimization, they improve source localization and obtain quantitative intensity estimates, demonstrating accuracy in terms of spatial separation through numerical simulations.
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.