Regularising Inverse Problems with Generative Machine Learning Models
- URL: http://arxiv.org/abs/2107.11191v1
- Date: Thu, 22 Jul 2021 15:47:36 GMT
- Title: Regularising Inverse Problems with Generative Machine Learning Models
- Authors: Margaret Duff, Neill D. F. Campbell, Matthias J. Ehrhardt
- Abstract summary: We consider the use of generative models in a variational regularisation approach to inverse problems.
The success of generative regularisers depends on the quality of the generative model.
We show that the success of solutions restricted to lie exactly in the range of the generator is highly dependent on the ability of the generative model.
- Score: 9.971351129098336
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Deep neural network approaches to inverse imaging problems have produced
impressive results in the last few years. In this paper, we consider the use of
generative models in a variational regularisation approach to inverse problems.
The considered regularisers penalise images that are far from the range of a
generative model that has learned to produce images similar to a training
dataset. We name this family \textit{generative regularisers}. The success of
generative regularisers depends on the quality of the generative model and so
we propose a set of desired criteria to assess models and guide future
research. In our numerical experiments, we evaluate three common generative
models, autoencoders, variational autoencoders and generative adversarial
networks, against our desired criteria. We also test three different generative
regularisers on the inverse problems of deblurring, deconvolution, and
tomography. We show that the success of solutions restricted to lie exactly in
the range of the generator is highly dependent on the ability of the generative
model but that allowing small deviations from the range of the generator
produces more consistent results.
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