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Learning Filter Functions in Regularisers by Minimising Quotients [code (Apollo)] [paper (arXiv)]

Researchers: Martin Benning, Guy Gilboa, Joana Sarah Grah, Carola-Bibiane Schönlieb

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most learning approaches, however, only aim at fitting parametrised models to favourable training data whilst ignoring misfit training data completely. In this paper, we follow up on the idea of learning parametrised regularisation functions by quotient minimisation as established in [2]. We extend the model therein to include higher-dimensional filter functions to be learned and allow for fit- and misfit-training data consisting of multiple functions. We first present results resembling behaviour of well-established derivative-based sparse regularisers like total variation or higher-order total variation in one-dimension. Our second and main contribution is the introduction of novel families of non-derivative-based regularisers. This is accomplished by learning favourable scales and geometric properties while at the same time avoiding unfavourable ones.

Related Publications 

Learning filter functions in regularisers by minimising quotients
M Benning, G Gilboa, JS Grah, C Schoenlieb – Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2017) 10302 LNCS, 511
Learning parametrised regularisation functions via quotient minimisation
M Benning, G Gilboa, C-B Schönlieb – Proceedings in Applied Mathematics and Mechanics (2016) 16, 933