Building firmly nonexpansive convolutional neural networks

Matthieu Terris, Audrey Repetti, Jean-Christophe Pesquet, Yves Wiaux

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Abstract

Building nonexpansive Convolutional Neural Networks (CNNs) is a challenging problem that has recently gained a lot of attention from the image processing community. In particular, it appears to be the key to obtain convergent Plug-and-Play algorithms. This problem consists in controlling the Lipschitz constant of the convolutional layers. Interestingly, this problem has also been investigated for Generative Adversarial Networks to improve robustness to adversarial perturbations. However, to the best of our knowledge, no efficient method has been developed yet to build nonexpansive CNNs. In this paper, we develop an optimization algorithm that can be incorporated in the training of a network to ensure the nonexpansiveness of its convolutional layers. This is shown to allow us to build firmly nonexpansive CNNs. We apply the proposed approach to train a CNN for an image denoising task and show its effectiveness through simulations.
Original languageEnglish
Title of host publicationICASSP 2020 - IEEE International Conference on Acoustics, Speech and Signal Processing
PublisherIEEE
Pages8658-8662
Number of pages5
ISBN (Electronic)9781509066315
DOIs
Publication statusPublished - 14 May 2020
Event45th IEEE International Conference on Acoustics, Speech and Signal Processing 2020 - Barcelona, Spain
Duration: 4 May 20208 May 2020
https://2020.ieeeicassp.org/

Publication series

NameIEEE International Conference on Acoustics, Speech and Signal Processing
ISSN (Electronic)2379-190X

Conference

Conference45th IEEE International Conference on Acoustics, Speech and Signal Processing 2020
Abbreviated titleICASSP 2020
CountrySpain
CityBarcelona
Period4/05/208/05/20
Internet address

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  • Cite this

    Terris, M., Repetti, A., Pesquet, J-C., & Wiaux, Y. (2020). Building firmly nonexpansive convolutional neural networks. In ICASSP 2020 - IEEE International Conference on Acoustics, Speech and Signal Processing (pp. 8658-8662). (IEEE International Conference on Acoustics, Speech and Signal Processing). IEEE. https://doi.org/10.1109/ICASSP40776.2020.9054731