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Nonlinearity in inverse problems poses great challenges in terms of analysis and numerical solution. Among those, bilinear and quadratic problems cover important imaging applications such as blind deconvolution, parallel MRI, and de-autoconvolution, while still possessing sufficient structure to allow for a dedicated treatment. Recently, progress has been made in exploiting this structure, using variational methods as well as compressed sensing techniques, to develop new solution strategies for various practical instances of this problem class. The proposed minisymposium will bring together experts on bilinear and quadratic inverse problems in imaging to discuss recent developments and exchange the aforementioned new ideas.