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

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STSW01 - Theoretical and algorithmic underpinnings of Big Data

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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