Ilker Kocyigit

We present a novel algorithm for high resolution coherent imaging of sound sources in random scattering media using time resolved measurements of the acoustic pressure at an array of receivers. The sound waves travel a long distance between the sources and receivers so that they are significantly affected by scattering in the random medium. We model the scattering effects by large random wavefront distortions, but the results extend to stronger effects, as long as the waves retain some coherence i.e., before the onset of wave diffusion. It is known that scattering in random media can be mitigated in imaging using coherent interferometry (CINT). This method introduces a statistical stabilization in the image formation, at the cost of image blur. We show how to modify the CINT method in order to image wave sources that are too close to each other to be distinguished by CINT alone. We introduce the algorithm from first principles and demonstrate its performance with numerical simulations.

We study a multiple measurement vector (MMV) approach to synthetic aperture radar (SAR) imaging of scenes with direction-dependent reflectivity and with polarization diverse measurements. The unknown reflectivity is represented by a matrix with row support corresponding to the location of the scatterers in the scene and columns corresponding to measurements gathered from different subapertures or different polarization of the waves. The MMV methodology is used to estimate the reflectivity matrix by inverting in an appropriate sense the linear system of equations that models the SAR data. We introduce a resolution analysis of imaging with MMV, which takes into account the sparsity of the imaging scene, the separation of the scatterers, and the diversity of the measurements. The results of the analysis are illustrated with some numerical simulations.

We study a multiple measurement vector (MMV) approach to synthetic aperture radar (SAR) imaging of scenes with direction dependent reflectivity and with polarization diverse measurements. The data are gathered by a moving transmit- receive platform which probes the imaging scene with signals and records the backscattered waves. The unknown reflectivity is represented by a matrix with row support corresponding to the location of the scatterers in the scene, and columns corresponding to measurements gathered from different sub-apertures, or different polarization of the waves. The MMV methodology is used to estimate the reflectivity matrix by inverting in an appropriate sense the linear system of equations that models the SAR data. We obtain a resolution analysis of SAR imaging with MMV, which takes into account the sparsity of the imaging scene, the separation of the scatterers and the diversity of the measurements. The results of the analysis are illustrated with some numerical simulations.

This paper surveys inverse problems arising in several coupled-physics imaging modalities for both medical and geophysical purposes. These include Photo-acoustic Tomography (PAT), Thermo-acoustic Tomography (TAT), Electro-Seismic Conversion, Transient Elastrography (TE) and Acousto-Electric Tomography (AET). These inverse problems typically consists of multiple inverse steps, each of which corresponds to one of the wave propagations involved. The review focuses on those steps known as the inverse problems with internal data, in which the complex geometrical optics (CGO) solutions to the underlying equations turn out to be useful in showing the uniqueness and stability in determining the desired information.

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....

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.