Lazzaretti, M;
Kereta, Z;
Estatico, C;
Calatroni, L;
(2023)
Stochastic Gradient Descent for Linear Inverse Problems in Variable Exponent Lebesgue Spaces.
In:
International Conference on Scale Space and Variational Methods in Computer Vision SSVM 2023: Scale Space and Variational Methods in Computer Vision.
(pp. pp. 457-470).
Springer, Cham
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Abstract
We consider a stochastic gradient descent (SGD) algorithm for solving linear inverse problems (e.g., CT image reconstruction) in the Banach space framework of variable exponent Lebesgue spaces ℓ(pn)(R). Such non-standard spaces have been recently proved to be the appropriate functional framework to enforce pixel-adaptive regularisation in signal and image processing applications. Compared to its use in Hilbert settings, however, the application of SGD in the Banach setting of ℓ(pn)(R) is not straightforward, due, in particular to the lack of a closed-form expression and the non-separability property of the underlying norm. In this manuscript, we show that SGD iterations can effectively be performed using the associated modular function. Numerical validation on both simulated and real CT data show significant improvements in comparison to SGD solutions both in Hilbert and other Banach settings, in particular when non-Gaussian or mixed noise is observed in the data.
| Type: | Proceedings paper |
|---|---|
| Title: | Stochastic Gradient Descent for Linear Inverse Problems in Variable Exponent Lebesgue Spaces |
| Event: | Scale Space and Variational Methods in Computer Vision 9th International Conference, SSVM 2023 |
| ISBN-13: | 9783031319747 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-031-31975-4_35 |
| Publisher version: | https://doi.org/10.1007/978-3-031-31975-4_35 |
| 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: | Iterative regularisation, Stochastic gradient descent, Inverse problems in Banach spaces, Computed Tomography |
| 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 Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10173714 |
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