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Multi-Mathematics for Imaging and Optimal Design Under Uncertainty

Final Report Summary - MULTIMOD (Multi-Mathematics for Imaging and Optimal Design Under Uncertainty)

In MULTIMOD, novel mathematical tools and efficient inversion methods to address emerging modalities in medical imaging, nondestructive testing, and environmental inverse problems have been developed. MULTIMOD have synergized asymptotic imaging, stochastic modelling, and mathematical analysis of both deterministic and stochastic wave propagation phenomena in complex and resonant media in order to go further in the field of mathematical imaging and solve the most challenging problems posed by the new imaging modalities and superresolution techniques. A new classification based approach in imaging has been introduced. Mathematical and numerical frameworks for a variety of very promising hybrid medical technologies as well as electrosensing, echolocation, and eddy current imaging have been developed. A theory for super-focusing and super-resolution of waves in resonant and high contrast materials has been established. It sheds light on the mechanism of the extraordinary wave properties of metamaterials, which include bubbly fluid near Minnaert resonant frequencies and nanoparticles near their plasmonic resonances. An innovative approach to interdisciplinary research and training in applied mathematics to best meet the challenges of emerging imaging technologies has been developed. A new generation of brilliant applied mathematicians has been trained to master all the mathematical and statistical aspects of modern imaging modalities.