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Learning regularization parameters of inverse problems via deep neural networks:Paper
- Source :
- Afkham, B M, Chung, J & Chung, M 2021, ' Learning regularization parameters of inverse problems via deep neural networks : Paper ', Inverse Problems, vol. 37, no. 10, 105017 . https://doi.org/10.1088/1361-6420/ac245d
- Publication Year :
- 2021
-
Abstract
- In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the mapping from observation data to regularization parameters. Once the network is trained, regularization parameters for newly obtained data can be computed by efficient forward propagation of the DNN. We show that a wide variety of regularization functionals, forward models, and noise models may be considered. The network-obtained regularization parameters can be computed more efficiently and may even lead to more accurate solutions compared to existing regularization parameter selection methods. We emphasize that the key advantage of using DNNs for learning regularization parameters, compared to previous works on learning via optimal experimental design or empirical Bayes risk minimization, is greater generalizability. That is, rather than computing one set of parameters that is optimal with respect to one particular design objective, DNN-computed regularization parameters are tailored to the specific features or properties of the newly observed data. Thus, our approach may better handle cases where the observation is not a close representation of the training set. Furthermore, we avoid the need for expensive and challenging bilevel optimization methods as utilized in other existing training approaches. Numerical results demonstrate the potential of using DNNs to learn regularization parameters.<br />27 pages, 16 figures
- Subjects :
- FOS: Computer and information sciences
Computer Science - Machine Learning
Bilevel optimization
010103 numerical & computational mathematics
01 natural sciences
Regularization (mathematics)
Theoretical Computer Science
Machine Learning (cs.LG)
Bayes' theorem
Design objective
Deep neural networks
Regularization
FOS: Mathematics
Mathematics - Numerical Analysis
0101 mathematics
Representation (mathematics)
Mathematical Physics
Mathematics
Applied Mathematics
Supervised learning
Deep learning
Numerical Analysis (math.NA)
Inverse problem
Computer Science Applications
010101 applied mathematics
Optimal experimental design
Signal Processing
Minification
Algorithm
Hyperparameter selection
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Afkham, B M, Chung, J & Chung, M 2021, ' Learning regularization parameters of inverse problems via deep neural networks : Paper ', Inverse Problems, vol. 37, no. 10, 105017 . https://doi.org/10.1088/1361-6420/ac245d
- Accession number :
- edsair.doi.dedup.....745a107e397085fb925440daa2e55f84