Towards the design of task-adapted models for inverse imaging problems

L. Calatroni, C. Cao, J. C. De Los Reyes, C.-B. Schönlieb, T. Valkonen, Bilevel approaches for learning of variational imaging models, RADON book series, vol. 18 on Variational Methods, (2016).
Large-scale learning, variational image reconstruction, non-smooth and non-convex optimisation, bilevel learning.
Data-driven learning approaches are becoming nowadays the reference paradigms for the design and the solution of a large class of reconstruction problems arising in several imaging applications such as biological imaging. In their general form, such methods compute the optimal ingredients of the model by exploring information in the training data with respect to some fixed quality measure, so as to estimate the degradation process (noise, blur, deformation…) in a robust and efficient way by means of large-scale optimisation techniques. However, the notion of “optimality” used to tailor the best model is often intrinsically ambiguous since it strongly depends on the objectives of the task performed which could range from image enhancement to object detection, e.g., in microscopy imaging. The general task becomes then to optimise the optimisers, which naturally leads to a two-level non-smooth and non-convex optimisation problem, which can accommodate a wide variety of advanced image reconstruction models. These characteristics pose severe limitations from the point of view of numerical efficiency and problem complexity. 
As a newly recruited CNRS researcher, Luca Calatroni's research project within the Morpheme project (SIS research group) is to unify data- and application-driven optimisation in one single recipe and extend advanced optimisation strategies to solve this two-level problem with a specific focus on fluorescence microscopy applications.