"The aim of this interdisciplinary project is to develop new mathematical and statistical tools, probabilistic approaches, and inversion and optimal design methods to address emerging modalities in medical imaging, nondestructive testing, and environmental inverse problems. It merges the complementary expertise of the investigators in order to make a breakthrough in the field ofmathematical imaging and optimal design by solving the most challenging problems posed by new imaging modalities. The PI and Co-PI are leading experts in their respective fields (appliedanalysis and probability) and their researches have very strong interdisciplinary nature.The goal of this project is to synergize asymptotic imaging, stochastic modelling, and analysis of both deterministic and stochastic wave propagation phenomena. We want to throw a bridge across the deterministic and stochastic aspects and tools of mathematical imaging. This requires a deep understanding of the different scales in the physical problem, an accurate modelling of the noise sources, and fine mathematical analysis of complex phenomena. The emphasis of this project will be put on deriving for each of the challenging imaging problems that we will consider, the best possible imaging functionals in the sense of stability and resolution. For optimal design problems, wewill evaluate the effect of uncertainties on the geometrical or physical parameters and design accurate optimal design methodologies.In this project, we will build an exceptional interdisciplinary research and an innovative approach to training in applied mathematics. We will train a new generation of applied mathematicians who will master both the probabilistic and analytical tools to best meet the challenges of emerging technologies."