Deep learning model-aware regulatization with applications to Inverse Problems

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Deep learning model-aware regulatization with applications to Inverse Problems

Amjad, J; Lyu, Z; Rodrigues, MRD; (2021) Deep learning model-aware regulatization with applications to Inverse Problems. IEEE Transactions on Signal Processing , 69 pp. 6371-6385. 10.1109/TSP.2021.3125601. Green open access

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Abstract

There are various inverse problems – including reconstruction problems arising in medical imaging - where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask whether such knowledge of the forward operator can be exploited in deep learning approaches increasingly used to solve inverse problems. In this paper, we provide one such way via an analysis of the generalisation error of deep learning approaches to inverse problems. In particular, by building on the algorithmic robustness framework, we offer a generalisation error bound that encapsulates key ingredients associated with the learning problem such as the complexity of the data space, the size of the training set, the Jacobian of the deep neural network and the Jacobian of the composition of the forward operator with the neural network. We then propose a ‘plug-and-play’ regulariser that leverages the knowledge of the forward map to improve the generalization of the network. We likewise also use a new method allowing us to tightly upper bound the Jacobians of the relevant operators that is much more computationally efficient than existing ones. We demonstrate the efficacy of our model-aware regularised deep learning algorithms against other state-of-the-art approaches on inverse problems involving various sub-sampling operators such as those used in classical compressed sensing tasks, image super-resolution problems and accelerated Magnetic Resonance Imaging (MRI) setups.

Type:	Article
Title:	Deep learning model-aware regulatization with applications to Inverse Problems
Open access status:	An open access version is available from UCL Discovery
DOI:	10.1109/TSP.2021.3125601
Publisher version:	https://doi.org/10.1109/TSP.2021.3125601
Language:	English
Additional information:	This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords:	Deep learning, generalization error, Jacobian, inverse problems, regularization, robustness
UCL classification:	UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI:	https://discovery.ucl.ac.uk/id/eprint/10138190