Collaborative Research: Improved Algorithms for Multiwave Imaging in Complex Media: Theory and Computation

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Improved imaging techniques are necessary to guide and inform increasingly complex surgical procedures. For example, cardiac bypass surgeries are required for infants born with congenital heart defects; however, approximately 50% of children develop brain injury perioperatively, leading to the damaging complications for survivors of congenital heart disease. Improved cerebral imaging techniques are needed to evaluate the effects of surgical procedures on brain perfusion. One of the most promising techniques for cerebral imaging are multiwave imaging methods such as photo-acoustic and thermo-acoustic tomography, which combine properties of different waves to obtain high contrast and resolution unattainable by traditional modalities. This project is motivated by the possible application of multiwave imaging to monitor cerebral blood perfusion in infants. It aims to incorporate the complexity of media properties in the head (brain, vasculature, blood, cerebrospinal fluid, skull, skin) into these imaging techniques, while making these techniques more robust to noise and uncertainty. The goals of this project are both theoretical and computational. The first is to identify general assumptions under which the photo-acoustic measurements render the simultaneous recovery of the internal source and the wave speed. This will be accomplished by expanding the mathematical theory concerning the simultaneous recovery of acoustic sources and media properties, which is one of the main open questions regarding photo-, thermo- and magneto- acoustic imaging. Based on preliminary work, the investigators have relaxed a-priori conditions under which simultaneous recovery is possible. The next step is to determine which conditions are essential and which ones can be removed. The second goal is computational and uses the intrinsic property of the photo-acoustic effect, which produces high contrast pressure profiles. The aim is to design novel discontinuous Galerkin methods for accurate, low dispersion simulations of high contrast pressure waves for use in new imaging algorithms. These methods are designed to achieve high performance on GPU architectures in the presence of realistic media and geometries. The third goal is to incorporate these new developments into PDE-constrained optimization algorithms, which, in addition to approximating the unknown wave speed of the medium, will also provide robustness with respect to noise and lack of information.