To Be or Not to Be Stable, That Is the Question: Understanding Neural Networks for Inverse Problems
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| Název: | To Be or Not to Be Stable, That Is the Question: Understanding Neural Networks for Inverse Problems |
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| Autoři: | Davide Evangelista, Elena Loli Piccolomini, Elena Morotti, James G. Nagy |
| Zdroj: | SIAM Journal on Scientific Computing. 47:C77-C99 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Society for Industrial & Applied Mathematics (SIAM), 2025. |
| Rok vydání: | 2025 |
| Témata: | FOS: Computer and information sciences, Computer Science - Machine Learning, neural networks stability, linear inverse problems, deep learning algorithms, image deblurring, trade-off accuracy stability, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Mathematics - Numerical Analysis, 02 engineering and technology, Numerical Analysis (math.NA), 65K10, 68T07, 68U10, Machine Learning (cs.LG) |
| Popis: | The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based on deep learning overwhelm the more traditional model-based approaches in performance, but they typically suffer from instability with respect to data perturbation. In this paper, we theoretically analyze the trade-off between stability and accuracy of neural networks, when used to solve linear imaging inverse problems for not under-determined cases. Moreover, we propose different supervised and unsupervised solutions to increase the network stability and maintain a good accuracy, by means of regularization properties inherited from a model-based iterative scheme during the network training and pre-processing stabilizing operator in the neural networks. Extensive numerical experiments on image deblurring confirm the theoretical results and the effectiveness of the proposed deep learning-based approaches to handle noise on the data. 21 pages, 6 figure. Paper will be sent for publication on a journal soon. This is a preliminary version, updated versions will be uploaded on ArXiv |
| Druh dokumentu: | Article |
| Popis souboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/23m1586872 |
| DOI: | 10.48550/arxiv.2211.13692 |
| Přístupová URL adresa: | http://arxiv.org/abs/2211.13692 https://epubs.siam.org/doi/10.1137/23M1586872 https://doi.org/10.1137/23M1586872 https://hdl.handle.net/11585/1009952 |
| Rights: | CC BY |
| Přístupové číslo: | edsair.doi.dedup.....f0a21862f88c1413550b1f0c99a87b0a |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based on deep learning overwhelm the more traditional model-based approaches in performance, but they typically suffer from instability with respect to data perturbation. In this paper, we theoretically analyze the trade-off between stability and accuracy of neural networks, when used to solve linear imaging inverse problems for not under-determined cases. Moreover, we propose different supervised and unsupervised solutions to increase the network stability and maintain a good accuracy, by means of regularization properties inherited from a model-based iterative scheme during the network training and pre-processing stabilizing operator in the neural networks. Extensive numerical experiments on image deblurring confirm the theoretical results and the effectiveness of the proposed deep learning-based approaches to handle noise on the data.<br />21 pages, 6 figure. Paper will be sent for publication on a journal soon. This is a preliminary version, updated versions will be uploaded on ArXiv |
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| ISSN: | 10957197 10648275 |
| DOI: | 10.1137/23m1586872 |