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Learning from mistakes - learning optimally sparse image filters by quotient minimisation

Presented by: 
Carola-Bibiane Schönlieb
Wednesday 17th January 2018 - 11:45 to 12:30
INI Seminar Room 1
Co-authors: Martin Benning (University of Cambridge), Guy Gilboa (Technion, Haifa), Joana Grah (University of Cambridge)

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 ig- noring misfit training data completely. In this talk, we fol- low up on the idea of learning parametrised regularisation functions by quotient minimisation. We consider one- and higher-dimensional filter functions to be learned and allow for fit- and misfit-training data consisting of multiple func- tions. We first present results resembling behaviour of well- established derivative-based sparse regularisers like total variation or higher-order total variation in one-dimension. Then, we introduce 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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons