Journal
SCALE SPACE AND VARIATIONAL METHODS IN COMPUTER VISION, SSVM 2017
Volume 10302, Issue -, Pages 511-523Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/978-3-319-58771-4_41
Keywords
Regularisation learning; Non-linear eigenproblem; Sparse regularisation; Generalised inverse power method
Categories
Funding
- Leverhulme Trust
- Newton Trust
- Israel Science Foundation [718/15]
- NIHR Cambridge Biomedical Research Centre
- Leverhulme Trust project
- EPSRC [EP/M00483X/1]
- EPSRC centre [EP/N014588/1]
- Cantab Capital Institute for the Mathematics of Information
- CHiPS (Horizon RISE project grant)
- EPSRC [EP/M00483X/1, EP/N014588/1] Funding Source: UKRI
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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 [3]. 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.
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