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Inverse problems appear in several fields of science and technology, including geophysics, bioimaging, material science, etc. and they require specific mathematical techniques to handle ill-posed problems. While fundamental results on uniqueness and stability of inverse problems have been obtained by mathematicians, other scientific communities seldom profit from these advances. Instead, practical approaches to inverse problems in geophysics are often based on modifications and generalizations of the least-squares method and possibly on stochastic approaches, e.g., when set in a Bayesian framework. A significant step forward for scientific research in geophysics requires that the theory and application of inverse problems “meet each other” in an open forum where both early-stage researchers and senior scientists are brought together with the aim of sharing their diverse scientific background and expertise in the fields of inverse problems, imaging and Earth exploration.