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.

Blind Demixing and Deconvolution at Near-Optimal Rate

Dominik Stoeger (Technical University of Munich)

Calibrationless Reconstruction Methods in Magnetic Resonance Imaging

Martin Uecker (University Medical Center Göttingen)

Regularization of bilinear and quadratic inverse problems by tensorial lifting

Robert Beinert (University of Graz)

Organizers:

Kristian Bredies (Universität Graz)

Felix Krahmer (Technical University of Munich, Department of Mathematics)

Keywords:

compressive imaging, image deblurring, image reconstruction, inverse problems, nonlinear optimization, stochastic processes