Bilevel approaches for learning of variational imaging models

By Luca Calatroni, Cao Van Chung, J. D. L. Reyes, Carola-Bibiane Schönlieb, Tuomo Valkonen. 2015

100 citations recorded by the source corpus.

We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space. The paper covers both analytical and numerical techniques. Analytically, we include results on the existence and structure of minimisers, as well as optimality conditions for their characterisation. Based on this information, Newton type methods are studied for the solution of the problems at hand, combining them with sampling techniques in case of large databases. The computational verification of the developed techniques is extensively documented, covering instances with different type of regularisers, several noise models, spatially dependent weights and large image databases.

Subfields: Computer Vision and Pattern Recognition, Ocean Engineering, Radiology, Nuclear Medicine and Imaging

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Vision and Pattern Recognition

1. Luc Van Gool
2. Jitendra Malik
3. Bernt Schiele
4. Ming-Hsuan Yang
5. Dacheng Tao
6. Trevor Darrell
7. Cordelia Schmid
8. Xiaogang Wang

In Ocean Engineering

1. David Kristjanson Duvenaud
2. Thomas Brox
3. Roger Baker Grosse
4. Fabian Pedregosa

In Radiology, Nuclear Medicine and Imaging

1. Ozan Öktem
2. Thomas Brox
3. Thomas Pock
4. Roger Baker Grosse
5. Fabian Pedregosa
6. René Ranftl
7. Jonas Adler
8. Jong Chul Ye

Citations in the corpus

• Hyperparameter optimization with approximate gradient (2016, methodology): “This is the iterative differentiation approach from (Domke, 2012), using the same inner-optimization algorithm as H OAG .”
• Techniques for Gradient-Based Bilevel Optimization with Non-smooth Lower Level Problems (2016, methodology): “A variational formulation for learning a good noise model was addressed in [34] in a PDE-constrained optimization framework, with some follow-up works [5,33,6].”
• Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions (2019, methodology): “, 2002; Seeger, 2007), and image reconstruction (Kunisch & Pock, 2013; Calatroni et al., 2015).”
• Solving ill-posed inverse problems using iterative deep neural networks (2017, background): “Some work has been done in selecting an optimal parameter using learning [8].”