The talks in our minisymposium discuss numerical methods and practise of imaging problems that are linked to measurements in a non-linear fashion. This linkage take, for instance, the form of a control constraint on the solution of an optimisation problem. As an example, the constraint can arise through a PDE modelling the relationship of boundary measurements to desired interior data; such imaging modalities include various forms of electrical, optical, and acoustic tomography. The linkage can also arise from the desire to optimise, to train, an inner imaging model to available true data or fitness functions. The inner model can take the form of a non-linear neural network, or an optimisation problem itself. While the former needs to mention, the latter methodology has also gained significant popularity as an approach to optimise conventional, more analytically justified imaging models to expected data.

Learning neural field equations for brain imaging

Christoph Brune (University of Twente)

A New Variational Approach for Limited Angle Tomography

Rob Tovey (University of Cambridge)

Total variation priors in electrical impedance tomography

Aku Seppänen (University of Eastern Finland)

A semi-infinite bilevel optimization approach for spatially-dependent parameter selection in total generalized variation image denoising

Kateryn Herrera (Escuela Politécnica Nacional)

Accelerated primal-dual methods for nonlinear inverse problems

Stanislav Mazurenko (University of Liverpool)

A two-point gradient method for nonlinear ill-posed problems

Simon Hubmer (Johannes Kepler University Linz)

A fast non regularized numerical algorithm for solving bilevel denoising problems

David Villacis (Escuela Politécnica Nacional)

Preconditioners for PDE-constrained optimization problems, with application to image metamorphosis

John Pearson (University of Edinburgh)

Organizers:

Juan Carlos De Los Reyes (Escuela Politécnica Nacional)

Tuomo Valkonen (University of Liverpool)

Keywords:

image reconstruction, inverse problems, machine learning, nonlinear optimization